| 单词 | logarithm |
| 例句 | “You use logarithms, you twit! How could you forget that?” October Sky 1999-04-01T00:00:00Z The logarithm of a number is simply the power to which 10 must be raised to equal the number in question. Innumeracy: Mathematical Illiteracy and Its Consequences 1988-01-01T00:00:00Z Like the Richter scale, the proposed index would be logarithmic, so what follows is a little detour to review for the innumerate those dreaded monsters from high school algebra: logarithms. Innumeracy: Mathematical Illiteracy and Its Consequences 1988-01-01T00:00:00Z The safety index associated with automobile driving is thus a relatively low 3.7, the logarithm of 5,300. Innumeracy: Mathematical Illiteracy and Its Consequences 1988-01-01T00:00:00Z For numbers between powers of 10, the logarithm is between the two nearest powers of 10. Innumeracy: Mathematical Illiteracy and Its Consequences 1988-01-01T00:00:00Z In 1944, The New York Times said he lisped in logarithms. Joel Kupperman, Scarred by Success as a ‘Quiz Kid,’ Dies at 83 2020-05-13T04:00:00Z In maths, ln refers to the natural logarithm of a number. Every human year not equivalent to seven dog years, scientists find 2020-07-02T04:00:00Z We did logarithms rather than “the new math”. You changed me: how my English teacher taught impeccable writing 2016-09-10T04:00:00Z "I think what people mistake for fate is actually a logarithm of interests and coincidences that brings you into the orbit of people who are like-minded; that's how you make your friends." Losers in love 2011-02-05T00:03:33Z She worked as a substitute teacher in 1952, teaching “quadratic equations, geometric construction, logarithms, polynomials, whatever they needed,” she explains. Review | Katherine Johnson of ‘Hidden Figures’ tells her story in her own words 2021-05-28T04:00:00Z Before calculators, people outsourced hairy arithmetic to reference books called logarithm tables. What Is Benford’s Law? Why This Unexpected Pattern of Numbers Is Everywhere 2023-05-08T04:00:00Z But unlike logarithms or formulas, there was no registry for sequences of numbers. The Most Boring Number in the World Is ... 2023-03-03T05:00:00Z You are unaware of this tremendous range in sound intensity because how your ears respond can be described approximately as the logarithm of intensity. College Physics for AP Courses 2015-08-12T00:00:00Z For example, the common logarithm of 100 is 2, because 10 must be raised to the second power to equal 100. Chemistry 2019-02-14T00:00:00Z The pH is calculated as the negative of the base 10 logarithm of this concentration. Biology for AP Courses 2022-06-09T00:00:00Z In 1881, astronomer Simon Newcomb noticed that early pages of logarithm tables, which correspond to numbers beginning with one, were grubby and worn compared with the pristine later pages. What Is Benford’s Law? Why This Unexpected Pattern of Numbers Is Everywhere 2023-05-08T04:00:00Z All three of these cases can be estimated by transforming the data to logarithms before running the regression. Introductory Business Statistics 2017-11-29T00:00:00Z How our ears perceive sound can be more accurately described by the logarithm of the intensity rather than directly to the intensity. College Physics for AP Courses 2015-08-12T00:00:00Z The common logarithm of a number less than 1 has a negative value. Chemistry 2019-02-14T00:00:00Z The natural logarithm of the reaction rate constant is a linear function of the inverse of the temperature in Kelvin degrees. Biology for AP Courses 2022-06-09T00:00:00Z Use the Properties of Logarithms to expand the logarithm . College Algebra with Corequisite Support 2020-09-23T00:00:00Z It is not possible to take the logarithm of a negative number in the set of real numbers. College Algebra 2021-12-21T00:00:00Z If we realize the logarithm is the exponent it makes the conversion easier. Intermediate Algebra 2020-05-06T00:00:00Z To obtain the common logarithm of a number, use the log button on your calculator. Chemistry 2019-02-14T00:00:00Z Using the negative logarithm to generate positive integers, high concentrations of hydrogen ions yield a low pH number, whereas low levels of hydrogen ions result in a high pH. Biology for AP Courses 2022-06-09T00:00:00Z Use the Properties of Logarithms to expand the logarithm . College Algebra with Corequisite Support 2020-09-23T00:00:00Z Any root expression can be rewritten as an expression with a rational exponent so that the power rule can be applied, making the logarithm easier to calculate. College Algebra 2021-12-21T00:00:00Z Now we will see that many characteristics of the logarithm function are simply ’mirror images’ of the characteristics of the corresponding exponential function. Intermediate Algebra 2020-05-06T00:00:00Z To obtain the natural logarithm of a number, use the ln button on your calculator. Chemistry 2019-02-14T00:00:00Z Note that this is a logarithm scale not a linear scale. Biology for AP Courses 2022-06-09T00:00:00Z Use the Properties of Logarithms to condense the logarithm . College Algebra with Corequisite Support 2020-09-23T00:00:00Z To evaluate this limit, we use the natural logarithm function. Calculus, Vol 2 2016-03-30T00:00:00Z Explain the difference between common logarithms and natural logarithms. Intermediate Algebra 2020-05-06T00:00:00Z The logarithm of a product of two numbers is the sum of the logarithms of the two numbers. Chemistry 2019-02-14T00:00:00Z Since this function uses natural e as its base, it is called the natural logarithm. Calculus, Volume 1 2016-03-30T00:00:00Z Use the Properties of Logarithms to condense the logarithm: College Algebra with Corequisite Support 2020-09-23T00:00:00Z Next we apply the quotient rule by subtracting the logarithm of the denominator from the logarithm of the numerator. Algebra and Trigonometry 2015-02-13T00:00:00Z While the natural logarithms are a special case of these properties, it is often helpful to also show the natural logarithm version of each property. Intermediate Algebra 2020-05-06T00:00:00Z The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers. Chemistry 2019-02-14T00:00:00Z Before solving some equations involving exponential and logarithmic functions, let’s review the basic properties of logarithms. Calculus, Volume 1 2016-03-30T00:00:00Z By doing so, we have derived the power rule for logarithms, which says that the log of a power is equal to the exponent times the log of the base. College Algebra with Corequisite Support 2020-09-23T00:00:00Z Here is an alternate proof of the quotient rule for logarithms using the fact that a reciprocal is a negative power: Algebra and Trigonometry 2015-02-13T00:00:00Z We again use the properties of logarithms to help us, but in reverse. Intermediate Algebra 2020-05-06T00:00:00Z The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. Chemistry 2019-02-14T00:00:00Z However, exponential functions and logarithm functions can be expressed in terms of any desired base b. Calculus, Volume 1 2016-03-30T00:00:00Z When given an equation of the form where and are algebraic expressions, we can use the one-to-one property of logarithms to solve the equation for the unknown. College Algebra with Corequisite Support 2020-09-23T00:00:00Z For the following exercises, condense each expression to a single logarithm using the properties of logarithms. Algebra and Trigonometry 2015-02-13T00:00:00Z In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Intermediate Algebra 2020-05-06T00:00:00Z Use logarithms to determine the value of the exponent m: Chemistry 2019-02-14T00:00:00Z As a result, the inverse hyperbolic functions involve the natural logarithm. Calculus, Volume 1 2016-03-30T00:00:00Z If the equation cannot be rewritten so that each side uses the same base, then apply the logarithm to each side and use properties of logarithms to solve. College Algebra with Corequisite Support 2020-09-23T00:00:00Z For the following exercises, suppose and Use the change-of-base formula along with properties of logarithms to rewrite each expression in terms of and Show the steps for solving. Algebra and Trigonometry 2015-02-13T00:00:00Z In the following exercises, use the Properties of Logarithms to expand the logarithm. Intermediate Algebra 2020-05-06T00:00:00Z One such scale that is very popular for chemical concentrations and equilibrium constants is based on the p-function, defined as shown where “X” is the quantity of interest and “log” is the base-10 logarithm: Chemistry 2019-02-14T00:00:00Z Since L’Hôpital’s rule applies to quotients, we use the natural logarithm function and its properties to reduce a problem evaluating a limit involving exponents to a related problem involving a limit of a quotient. Calculus, Volume 1 2016-03-30T00:00:00Z The one-to-one property cannot be used when each side of the equation cannot be rewritten as a single logarithm with the same base. College Algebra with Corequisite Support 2020-09-23T00:00:00Z Can the power property of logarithms be derived from the power property of exponents using the equation If not, explain why. Algebra and Trigonometry 2015-02-13T00:00:00Z In the following exercises, use the Properties of Logarithms to condense the logarithm. Intermediate Algebra 2020-05-06T00:00:00Z Because 60 lies between 10 and 100, which have logarithms of 1 and 2, respectively, the logarithm of 60 is 1.7782; that is, Chemistry 2019-02-14T00:00:00Z Substitution is often used to evaluate integrals involving exponential functions or logarithms. Calculus, Volume 1 2016-03-30T00:00:00Z Here’s the conversion formula the scientists came up with: Human age is equal to 16 multiplied by the natural logarithm of the dog’s age, plus 31. A better way to gauge ‘dog years’ 2022-04-22T04:00:00Z Use the definition of a logarithm to solve logarithmic equations. Algebra and Trigonometry 2015-02-13T00:00:00Z Now that we have the properties of logarithms, we have additional methods we can use to solve logarithmic equations. Intermediate Algebra 2020-05-06T00:00:00Z For example, the natural logarithm of 10 is 2.303; that is, Chemistry 2019-02-14T00:00:00Z We already examined exponential functions and logarithms in earlier chapters. Calculus, Volume 1 2016-03-30T00:00:00Z To accommodate the vast size differences, the researchers divided classes using a mathematical function called a logarithm: the average weight of organisms in one class differed by a factor of 10 from adjacent classes. All Ocean Life Follows This Massive Pattern—Except Where Humans Have Interfered 2022-03-30T04:00:00Z Use the one-to-one property of logarithms to solve logarithmic equations. Algebra and Trigonometry 2015-02-13T00:00:00Z Remember that logarithms are defined only for positive real numbers. Intermediate Algebra 2020-05-06T00:00:00Z Secondly, the defense’s objection is about those Apple logarithms adding data to an image such that it can be viewed in three dimensions or recreate what is not there. Rittenhouse trial judge still baffled by pinch-to-zoom 2021-11-12T05:00:00Z For purposes of this section, assume we have not yet defined the natural logarithm, the number e, or any of the integration and differentiation formulas associated with these functions. Calculus, Volume 1 2016-03-30T00:00:00Z In a simple statistical model, Manrubia and her colleagues showed that the average number of generations separating two random present-day individuals from a common genealogical ancestor depends on the logarithm of the relevant population’s size. Humans Are All More Closely Related Than We Commonly Think 2020-10-05T04:00:00Z When we have an equation with a base on either side, we can use the natural logarithm to solve it. Algebra and Trigonometry 2015-02-13T00:00:00Z You may have obtained a result that gives a logarithm of zero or a negative number. Intermediate Algebra 2020-05-06T00:00:00Z The language of mathematics, grounded in scientific notation, logarithms and orders of magnitude, allows us to grapple with the cosmos where words fall short, explains Burrows. How Mere Humans Manage to Comprehend the Vastness of the Universe 2019-10-11T04:00:00Z We begin the section by defining the natural logarithm in terms of an integral. Calculus, Volume 1 2016-03-30T00:00:00Z For small values of k, the fractional part of the base 2 logarithm of k moves around a lot. How Quickly Can You Fill Up a Circle? 2019-09-08T04:00:00Z Notice that, comparing the logarithm function and the exponential function, the input and the output are switched. Algebra and Trigonometry 2015-02-13T00:00:00Z Another strategy to use to solve logarithmic equations is to condense sums or differences into a single logarithm. Intermediate Algebra 2020-05-06T00:00:00Z While classmates dutifully calculated their answers to mathematical problems by use of the figures in tables of logarithms, Dr. Feigenbaum started by computing his own logarithms. Mitchell Feigenbaum, an architect of chaos theory, dies at 74 2019-07-12T04:00:00Z Note that if we use the absolute value function and create a new function ln |x|, we can extend the domain of the natural logarithm to include x < 0. Calculus, Volume 1 2016-03-30T00:00:00Z Even with heaping helpings of logarithms, trigonometry, and gumption, the number line is more unknown than known. The Unknowability of the Number Line 2019-01-12T05:00:00Z Q&A Can we take the logarithm of a negative number? Algebra and Trigonometry 2015-02-13T00:00:00Z When there are logarithms on both sides, we condense each side into a single logarithm. Intermediate Algebra 2020-05-06T00:00:00Z Beginning next week, Gard said, he plans to start where they left off, reviewing logarithms and teaching unit circles. ‘Protect us’: Two weeks after Valentine’s Day shooting, students return to class at Florida high school 2018-02-28T05:00:00Z Although we have called our function a “logarithm,” we have not actually proved that any of the properties of logarithms hold for this function. Calculus, Volume 1 2016-03-30T00:00:00Z But beneath it all he has the mathematics of merriment, the logarithms of laughter, at his fingers' ends. 100 years ago, Charlie Chaplin began work in his new studio 2018-01-26T05:00:00Z Also, we cannot take the logarithm of zero. Algebra and Trigonometry 2015-02-13T00:00:00Z In that case we often take the common logarithm or natural logarithm of both sides once the exponential is isolated. Intermediate Algebra 2020-05-06T00:00:00Z Like logarithms, or the zero, or exponential functions. The Hidden Depth in Math's Simple Puzzles 2018-01-17T05:00:00Z Note that the natural logarithm is one-to-one and therefore has an inverse function. Calculus, Volume 1 2016-03-30T00:00:00Z An economic adviser talked up the country’s technological achievements, which include the publication of an early volume of logarithm tables. Telling Slovenia and Slovakia Apart 2017-05-22T04:00:00Z In other words, the expression means We call a base-10 logarithm a common logarithm. Algebra and Trigonometry 2015-02-13T00:00:00Z When the exponential has base e, we use the natural logarithm. Intermediate Algebra 2020-05-06T00:00:00Z The size of the plotting symbols is proportional to the logarithm of the counting rate. The role of low-volatility organic compounds in initial particle growth in the atmosphere : Nature : Nature Publishing Group 2016-05-24T04:00:00Z As with part iv. of the logarithm properties, we can extend property iii. to irrational values of r, and we do so by the end of the section. Calculus, Volume 1 2016-03-30T00:00:00Z Against older siblings, he was said to be unbeatable in mathematical games by age 6 because of his knowledge of logarithms. Lloyd Shapley, who shared the 2012 Nobel Prize in economics, dies at 92 2016-03-14T04:00:00Z What is its relationship to a logarithm with base and how does the notation differ? Algebra and Trigonometry 2015-02-13T00:00:00Z In the following exercises, use the Quotient Property of Logarithms to write each logarithm as a sum of logarithms. Intermediate Algebra 2020-05-06T00:00:00Z The size of the plotting symbols is proportional to the logarithm of the counting rate. The role of low-volatility organic compounds in initial particle growth in the atmosphere : Nature : Nature Publishing Group 2016-05-24T04:00:00Z We then examine logarithms with bases other than e as inverse functions of exponential functions. Calculus, Volume 1 2016-03-30T00:00:00Z These big thinkers are now tackling a problem as complex as any logarithm - solving the Cleveland Browns. Brains amid brawn: Browns introduce front-office thinkers 2016-01-21T05:00:00Z In other words, logarithms give the cause for an effect. Algebra and Trigonometry 2015-02-13T00:00:00Z In the following exercises, use the Power Property of Logarithms to expand each logarithm. Intermediate Algebra 2020-05-06T00:00:00Z She worked with Hensley and about six of his classmates on logarithms, a mathematics function usually introduced in eighth- or ninth-grade algebra. Senior year mostly lost time for honor students at Normandy 2015-05-03T04:00:00Z This definition also allows us to generalize property iv. of logarithms and property iii. of exponential functions to apply to both rational and irrational values of r. Calculus, Volume 1 2016-03-30T00:00:00Z Think of it as a real-world check against the failing computer chip, the bad logarithm or a broken or snow-covered sensor. Why the Google Autonomous Car is Good for You 2014-05-29T04:00:00Z This means that logarithms have similar properties to exponents. Algebra and Trigonometry 2015-02-13T00:00:00Z When the base of the logarithm function is 10, we call it the common logarithmic function and the base is not shown. Intermediate Algebra 2020-05-06T00:00:00Z Numberphile recently posted a video about Log Tables, which explains how people used logarithms to multiply big numbers in the dark pre-calculator days. 10 Secret Trig Functions Your Math Teachers Never Taught You 2013-09-16T13:18:09.820Z Note that general logarithm functions can be written in terms of the natural logarithm. Calculus, Volume 1 2016-03-30T00:00:00Z "After five pictures it was like, 'Why stop?'" he said. logic lock-picking logarithm It's the butterflies. Quiz of the week's news 2013-07-04T23:31:00Z No. Keep in mind that we can only apply the logarithm to a positive number. Algebra and Trigonometry 2015-02-13T00:00:00Z If the base a of a logarithm is not shown, we assume it is 10. Intermediate Algebra 2020-05-06T00:00:00Z In other words, logarithms make multiplication into addition. If you wanted to multiply two numbers together using a log table, you would look up the logarithm of both numbers and then add the logarithms together. 10 Secret Trig Functions Your Math Teachers Never Taught You 2013-09-16T13:18:09.820Z Next, we use this formula to find a differentiation formula for a logarithm with base a. Calculus, Volume 1 2016-03-30T00:00:00Z One technique they use takes the logarithm of the death rate to keep things above the zero line and thereby eliminate any through-the-looking glass prospects. Gun Control: Searching Down Under for Change to Believe In 2012-12-20T17:45:00.327Z When can the one-to-one property of logarithms be used to solve an equation? Algebra and Trigonometry 2015-02-13T00:00:00Z In the following exercises, find the exact value of each logarithm without using a calculator. Intermediate Algebra 2020-05-06T00:00:00Z Then you’d use your log table to find out which number had that logarithm, and that was your answer. 10 Secret Trig Functions Your Math Teachers Never Taught You 2013-09-16T13:18:09.820Z The earlier treatment of logarithms and exponential functions did not define the functions precisely and formally. Calculus, Volume 1 2016-03-30T00:00:00Z I started to look for solutions to really understand human being and found a logarithm that uses cameras to understand people. Welcome to The Future: BlueBubbleLab and The Market Research of Tomorrow 2012-11-12T10:21:59Z For the following exercises, use logarithms to solve. Algebra and Trigonometry 2015-02-13T00:00:00Z The first two properties derive from the definition of logarithms. Intermediate Algebra 2020-05-06T00:00:00Z The secret trig functions, like logarithms, made computations easier. 10 Secret Trig Functions Your Math Teachers Never Taught You 2013-09-16T13:18:09.820Z The cornerstone of the development is the definition of the natural logarithm in terms of an integral. Calculus, Volume 1 2016-03-30T00:00:00Z Everything from Newton making sense of gravity and motion to Napier with logarithms and Harvey with blood circulation. Paralympics TV deals break new ground as ticket rush continues 2012-08-27T16:47:58Z Logarithmic equations can be written in an equivalent exponential form, using the definition of a logarithm. Algebra and Trigonometry 2015-02-13T00:00:00Z In the next example we could evaluate the logarithm by converting to exponential form, as we have done previously, but recognizing and then applying the properties saves time. Intermediate Algebra 2020-05-06T00:00:00Z Versine ranges between 0 and 2, so if you are using log tables to multiply with a versine, you don’t have to worry about the fact that the logarithm is not defined for negative numbers. 10 Secret Trig Functions Your Math Teachers Never Taught You 2013-09-16T13:18:09.820Z The function ex is then defined as the inverse of the natural logarithm. Calculus, Volume 1 2016-03-30T00:00:00Z A sharper linear relationship is evident after taking logarithms. Olympics 2012: the alternative medals table 2012-07-30T10:09:16Z Exponential equations can be written in their equivalent logarithmic form using the definition of a logarithm See Example 2. Algebra and Trigonometry 2015-02-13T00:00:00Z In the next example, apply the inverse properties of logarithms. Intermediate Algebra 2020-05-06T00:00:00Z Where he is not able to trace the direct relation of things he has recourse to his yard-stick and table of logarithms, which aid and facilitate his thought without predominating over it. Popular scientific lectures 2012-04-24T02:00:17.273Z General exponential functions are defined in terms of ex, and the corresponding inverse functions are general logarithms. Calculus, Volume 1 2016-03-30T00:00:00Z He left school at sixteen, after having mastered geometry and trigonometry, and having learned to use logarithms. Historic Fredericksburg The Story of an Old Town 2012-04-11T02:00:30.517Z Common logarithms can be evaluated mentally using previous knowledge of powers of See Example 5. Algebra and Trigonometry 2015-02-13T00:00:00Z Use the Quotient Property of Logarithms to write each logarithm as a difference of logarithms. Intermediate Algebra 2020-05-06T00:00:00Z Our musical notation is essentially a graphical representation of a piece of music in the form of curves, where the time is the abscissæ, and the logarithms of the number of vibrations the ordinates. Popular scientific lectures 2012-04-24T02:00:17.273Z Familiar properties of logarithms and exponents still hold in this more rigorous context. Calculus, Volume 1 2016-03-30T00:00:00Z Multiplication, involution, exponents, negative exponents, roots, and the use of exponents as logarithms. A System of Easy Lettering 2012-04-09T02:00:30.757Z When common logarithms cannot be evaluated mentally, a calculator can be used. Algebra and Trigonometry 2015-02-13T00:00:00Z In the following exercises, use the Product Property of Logarithms to write each logarithm as a sum of logarithms. Intermediate Algebra 2020-05-06T00:00:00Z The word has been sometimes, though rarely, used to denote the complement of a given logarithm; also the logarithmic cosine corresponding to a given logarithmic sine. Webster's Unabridged Dictionary 2012-03-24T02:00:23.513Z The number from which a mathematical table is constructed; as, the base of a system of logarithms. Webster's Unabridged Dictionary (2nd 100 Pages) 2012-03-24T02:00:19.387Z B. C. Five figure logarithms for general use. A System of Easy Lettering 2012-04-09T02:00:30.757Z Real-world exponential problems with base can be rewritten as a common logarithm and then evaluated using a calculator. Algebra and Trigonometry 2015-02-13T00:00:00Z In the following exercises, use properties of logarithms to write each logarithm as a sum of logarithms. Intermediate Algebra 2020-05-06T00:00:00Z However, the facts of the cosmos were on his side, but the calculations essential in testing his various hypotheses were of the most tedious nature, because logarithms were not yet known in his day. Astronomy: The Science of the Heavenly Bodies 2012-03-17T02:01:02.630Z Or the nerdy tech guy in the office who never watched a game and employed some logarithm to figure out the Final Four. Here's help for NCAA bracket-challenged 2012-03-14T01:13:00Z But as to eloquence, he knows no more about it than a table of logarithms. Sketches of Reforms and Reformers, of Great Britain and Ireland 2012-03-12T03:00:20.310Z We can use the quotient rule of logarithms to rewrite the log of a quotient as a difference of logarithms. Algebra and Trigonometry 2015-02-13T00:00:00Z In the following exercises, use the Properties of Logarithms to condense the logarithm. Intermediate Algebra 2020-05-06T00:00:00Z When he had a few moments for diversion, he not unfrequently employed them in looking over a book of logarithms, in which he always found recreation. Harper's New Monthly Magazine, Vol IV. No. XX. January, 1852. 2012-02-24T03:00:24.390Z Take up your table of logarithms and figure away until you are blind, and such an accident could not happen in as many thousand, billion, trillion, quintillion years as you can express by figures. The Works of Robert G. Ingersoll, Vol. 10 (of 12) Dresden Edition?Legal 2012-02-11T03:04:05.257Z Most people who talk on this point bring forward column after column of figures, and a man to understand it would have to be a walking table of logarithms. The Works of Robert G. Ingersoll, Vol. 8 (of 12) Dresden Edition?Political 2012-02-11T03:03:48.503Z We can use the power rule for logarithms to rewrite the log of a power as the product of the exponent and the log of its base. Algebra and Trigonometry 2015-02-13T00:00:00Z In the following exercises, use properties of logarithms to write each expression as a sum of logarithms, simplifying if possible. Intermediate Algebra 2020-05-06T00:00:00Z First I will review what we mean by logarithms. When Should I Use Logarithmic Scales in My Charts and Graphs? 2012-01-19T13:02:18Z The idea of logarithms arose in the mind of Napier from the wish to simplify the processes of multiplication and division, by making addition and subtraction take their place. Sir Thomas Urquhart of Cromartie, Knight 2012-01-19T03:00:21.953Z The electric and magnetic energies became unequal, and α started to increase very slowly, growing as the logarithm of time. Inconstant Constants 2011-12-31T05:15:18.567Z The rules of logarithms can also be used to condense sums, differences, and products with the same base as a single logarithm. Algebra and Trigonometry 2015-02-13T00:00:00Z In the following exercises, use the Properties of Logarithms to condense the logarithm, simplifying if possible. Intermediate Algebra 2020-05-06T00:00:00Z From the father of his inamorata he would have listened to the reading of a table of logarithms. Froth 2011-12-28T03:00:38.123Z The vast saving to mental labour by this simple and beautiful adjustment of numbers may be estimated by a glance at any collection of tables of logarithms. Sir Thomas Urquhart of Cromartie, Knight 2012-01-19T03:00:21.953Z He is well up in logarithms, and a capital arithmetician, I won’t say mathematician, though he knows something of mathematics as well. The Cruise of the Snowbird A Story of Arctic Adventure 2011-12-13T03:00:23.197Z We can solve exponential equations with base by applying the natural logarithm of both sides because exponential and logarithmic functions are inverses of each other. Algebra and Trigonometry 2015-02-13T00:00:00Z There are three more properties of logarithms that will be useful in our work. Intermediate Algebra 2020-05-06T00:00:00Z Her first two semesters in math, Nathaly got an 89 and an 86, but then fell apart on trigonometry, exponents and logarithms. On Education: Let?s Get Ready Offers Help for College Admissions 2011-11-21T03:37:17Z The former of these last-mentioned Epistles is signed by Sir Thomas, and consists of a glowing tribute of respect to Napier, the inventor of logarithms. Sir Thomas Urquhart of Cromartie, Knight 2012-01-19T03:00:21.953Z But it would be left to a fellow scientist, Augusta Ada King, Countess of Lovelace, to fully appreciate that his inventions were more than just tools for automatically tabulating logarithms and trigonometric functions. Computer Experts Building 1830s Babbage Analytical Engine 2011-11-07T22:34:10Z When given an equation of the form where is an algebraic expression, we can use the definition of a logarithm to rewrite the equation as the equivalent exponential equation and solve for the unknown. Algebra and Trigonometry 2015-02-13T00:00:00Z Our definition of logarithm shows us that a logarithm is the exponent of the equivalent exponential. Intermediate Algebra 2020-05-06T00:00:00Z It is easy to teach logarithms in the seventh school year, but it is not good policy to do so under present conditions. The Teaching of Geometry 2011-10-12T02:00:52.133Z He does this with all his passengers, he tells me, reduces the figures to logarithms, and works out the ship's course in decimals. Puppets at Large Scenes and Subjects from Mr Punch's Show 2011-09-19T02:00:13.900Z “I’m merely catching them for sport, you mouldy old logarithm,” replied Scott. Harry Milvaine The Wanderings of a Wayward Boy 2011-09-08T02:00:23.340Z When given an equation of the form where and are algebraic expressions, we can use the one- to-one property of logarithms to solve the equation for the unknown. Algebra and Trigonometry 2015-02-13T00:00:00Z Use the Product Property of Logarithms to write each logarithm as a sum of logarithms. Intermediate Algebra 2020-05-06T00:00:00Z This last term is defined as the logarithm of the ratio of one swing to the next succeeding swing, and a galvanometer of which the logarithmic decrement is large, is said to be highly damped. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 4 "G" to "Gaskell, Elizabeth" 2011-08-24T02:00:20.690Z They had not learned the use of logarithms, and were ignorant of fluxions. The Works of Daniel Webster, Volume 1 2011-07-27T02:00:32.830Z He had Euclid at his finger ends, while his knowledge of algebra and logarithms enabled him to solve in a few minutes the most difficult questions. Norfolk Annals A Chronological Record of Remarkable Events in the Nineteeth Century, Vol. 2 2011-05-25T02:00:19.650Z Use the definition of a logarithm to solve. Algebra and Trigonometry 2015-02-13T00:00:00Z We essentially take the exponent and throw it in front of the logarithm. Intermediate Algebra 2020-05-06T00:00:00Z There are two bases of logarithms in common use, the base 10 and the Napierian base e. The New Gresham Encyclopedia Volume 4, Part 3: Estremoz to Felspar 2011-04-14T02:00:59.373Z In the above formula ε is the base of the Napierian logarithms. Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 3 "Electrostatics" to "Engis" 2011-02-06T03:00:53.093Z Merchiston Academy, housed in the old castle of Napier, the inventor of logarithms, is another institution conducted on English public school lines. Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 10 "Echinoderma" to "Edward" 2011-01-19T03:00:19.027Z We read a logarithmic expression as, “The logarithm with base of is equal to ” or, simplified, “log base of is ” We can also say, “ raised to the power of is ” because logs are exponents. Algebra and Trigonometry 2015-02-13T00:00:00Z Use the Power Property of Logarithms to write each logarithm as a product of logarithms. Intermediate Algebra 2020-05-06T00:00:00Z If ax = N, x is said to be the logarithm of N to the base a. The New Gresham Encyclopedia Volume 4, Part 3: Estremoz to Felspar 2011-04-14T02:00:59.373Z Stockbridge et al. begin with Arrhenius plots, which relate the logarithm of the rate constant to the reciprocal of temperature. Editors' Choice 2011-01-06T19:25:03.183Z The computation can be very greatly abridged by the use of logarithms. A Text-Book of Astronomy 2011-01-05T03:00:57.347Z For example, the base 2 logarithm of 32 is 5, because 5 is the exponent we must apply to 2 to get 32. Algebra and Trigonometry 2015-02-13T00:00:00Z This means to write the logarithm as a sum or difference and without any powers. Intermediate Algebra 2020-05-06T00:00:00Z “That seemed such a change from the days of logarithms,” he said. Brian Marsden, Tracker of Comets, Dies at 73 2010-11-23T03:59:00Z The figure shows a plot of the population of the logarithm of 2009 metropolitan area populations against population rank. A Tale of Many Cities 2010-04-20T11:18:00Z Tags: exponential growth, folding paper, functions, logarithms If you were an avid television watcher in the 1980s, you may remember a clever show called “Moonlighting.” Power Tools 2010-03-28T23:57:00Z We can never take the logarithm of a negative number. Algebra and Trigonometry 2015-02-13T00:00:00Z The opposite of expanding a logarithm is to condense a sum or difference of logarithms that have the same base into a single logarithm. Intermediate Algebra 2020-05-06T00:00:00Z The invention of logarithms, the rise of analytical geometry, and the evolution of B. Cavalieri’s “indivisibles” into the infinitesimal calculus, all accomplished during the 17th century, immeasurably widened the scope of exact astronomy. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 7 "Arundel, Thomas" to "Athens" Also most fractions cannot be expressed exactly as decimals; and this is also the case for surds and logarithms, as well as for the numbers expressing certain ratios which arise out of geometrical relations. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" That pretty well sums up how many people feel about logarithms. Power Tools 2010-03-28T23:57:00Z Natural logarithms can be evaluated using a calculator Example 8. Algebra and Trigonometry 2015-02-13T00:00:00Z Because our calculators have keys for logarithms base 10 and base e, we will rewrite the Change-of-Base Formula with the new base as 10 or e. Intermediate Algebra 2020-05-06T00:00:00Z Decimal fractions were invented in the sixteenth century, and logarithms, embodying the last great advance in the science, in the seventeenth century. The New Gresham Encyclopedia. Vol. 1 Part 2 Amiel to Atrauli For a further explanation of logarithms, and for an explanation of the treatment of cases in which an antilogarithm is less than 1, see Logarithm. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" Most folks never use them again after high school, at least not consciously, and are oblivious to the logarithms hiding behind the scenes of their daily lives. Power Tools 2010-03-28T23:57:00Z We can use the product rule, the quotient rule, and the power rule together to combine or expand a logarithm with a complex input. Algebra and Trigonometry 2015-02-13T00:00:00Z We eliminate x = −9 as we cannot take the logarithm of a negative number. x = 9, Intermediate Algebra 2020-05-06T00:00:00Z If I might use a harsh metaphor, I should say he is made the logarithm of his true self, and in that shape is worked with the ease and satisfaction of logarithms. An Essay In Aid Of A Grammar Of Assent We take out log 2 from the table, halve it, and then find from the table the number of which this is the logarithm. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" Just as every office worker needs both a stapler and a staple remover, every mathematician needs exponential functions and logarithms. Power Tools 2010-03-28T23:57:00Z We can convert a logarithm with any base to a quotient of logarithms with any other base using the change-of-base formula. Algebra and Trigonometry 2015-02-13T00:00:00Z Since the exponential is isolated, take the logarithm of both sides. Intermediate Algebra 2020-05-06T00:00:00Z Mr. von Osten would have had a like experience if he had asked Hans concerning the value of Chinese coins or the logarithm of 1000. Clever Hans (The horse of Mr. Von Osten): A contribution to experimental animal and human psychology If we know n and N, then p is the logarithm of N to base n. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" That “six” is roughly the logarithm of these salaries, which in fact span the range from 5 to 6. Power Tools 2010-03-28T23:57:00Z The change-of-base formula is often used to rewrite a logarithm with a base other than 10 and as the quotient of natural or common logs. Algebra and Trigonometry 2015-02-13T00:00:00Z She, 224 herself, was not taking that course, for she preferred logarithms and abstruse calculations, to the marvels of the Parthenon. Dolly's College Experiences While he is going over his logarithms to know what should be done, the commonest seaman on board could set all to rights. Sporting Scenes amongst the Kaffirs of South Africa The calculation of a logarithm can be performed by successive divisions; evolution requires special methods. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" The difference of the logarithms of these numbers, rejecting the index, and taking only the four next figures, will give 690 fathoms, 4140 feet, for the height of Kathmandu above the Tariyani. An Account of The Kingdom of Nepal And of the Territories Annexed to this Dominion by the House of Gorkha When an exponential equation cannot be rewritten with a common base, solve by taking the logarithm of each side. Algebra and Trigonometry 2015-02-13T00:00:00Z On leaving school he took up mathematics as a specialty and invented a system of logarithms based on the number 12 instead of 10. Elementary Theosophy It was difficult to explain to these unmathematical minds the mysteries of “sights,” latitude and longitude, or the use of logarithms. Sporting Scenes amongst the Kaffirs of South Africa The above definitions of logarithms, &c., relate to cases in which n and p are whole numbers, and are generalized later. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" "With me life's logarithms share, Kate, that I cannot solve alone!" Punch, or, the London Charivari, Volume 98, March 8, 1890. Combining the skills learned in this and previous sections, we can solve equations that model real world situations, whether the unknown is in an exponent or in the argument of a logarithm. Algebra and Trigonometry 2015-02-13T00:00:00Z Instead of going into logarithms, Henry went into shorthand. A Great Man A Frolic It is much easier to become a navigator with the aid of modern instruments constructed with extreme accuracy, and with tables of logarithms, nautical almanacs, and admiralty charts. Christopher Columbus and His Monument Columbia being a concordance of choice tributes to the great Genoese, his grand discovery, and his greatness of mind and purpose Logarithms.—Multiplication, division, involution and evolution, when the results cannot be exact, are usually most simply performed, at any rate to a first approximation, by means of a table of logarithms. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" Among many others, the great Napier, the inventor of logarithms, might be produced as an instance of this remark. Travels in China, Containing Descriptions, Observations, and Comparisons, Made and Collected in the Course of a Short Residence at the Imperial Palace of Yuen-Min-Yuen, and on a Subsequent Journey through the Country from Pekin to Canton Common logarithms are used to measure the Richter Scale mentioned at the beginning of the section. Algebra and Trigonometry 2015-02-13T00:00:00Z He used logarithms, and proved the accuracy of his work by different methods. From Farm House to the White House The life of George Washington, his boyhood, youth, manhood, public and private life and services The invention of logarithms, by Baron Napier, of Merchistoun, was found to be of inestimable value to astronomers in facilitating and abbreviating the methods of astronomical calculation. The Astronomy of Milton's 'Paradise Lost' But the result of a rigid application of this principle would be that the calculation of the cost of 3 ℔ of tea at 2s. a ℔ would be deferred until after the study of logarithms. Encyclopaedia Britannica, 11th Edition, Volume 2, Slice 5 "Arculf" to "Armour, Philip" “But how did you manage about logarithms,” he said. By Conduct and Courage A Story of the Days of Nelson Scales for measuring the brightness of stars and the pH of acids and bases also use common logarithms. Algebra and Trigonometry 2015-02-13T00:00:00Z The logarithm of the total volume is recorded as a result of the addition of these three logarithms enumerated, and from this logarithm is expressed the total volume of air in liters. Respiration Calorimeters for Studying the Respiratory Exchange and Energy Transformations of Man By the use of logarithms, arithmetical computations which necessitated laborious application for several months could with ease be completed in as many days. The Astronomy of Milton's 'Paradise Lost' In after life I, of course, used logarithms for the higher branches of science. Personal Recollections, from Early Life to Old Age, of Mary Somerville Now let us work out the same problem by logarithms. Lectures in Navigation The major exception is that, because the logarithm of 1 is always 0 in any base, For other natural logarithms, we can use the key that can be found on most scientific calculators. Algebra and Trigonometry 2015-02-13T00:00:00Z But by the use of logarithms it may be quickly ascertained that the required quantity is very nearly 73-97/100 pints of wine left in the cask. The Canterbury Puzzles And Other Curious Problems Think of the English language, basic business methods, tables of logarithms, the Pythagorean theorem, Shakespeare's insights about human nature, the periodic table, Ohm's law, the sonnet form, the musical scale. The Public Domain Enclosing the Commons of the Mind They brought her a treatise on logarithms by the Rev. C.L. Stories of Authors, British and American Copy of another letter to clergyman; discovery tested by logarithms; reasons such as none but a knave or a sinner can resist. A Budget of Paradoxes, Volume II We can also find the natural logarithm of any power of using the inverse property of logarithms. Algebra and Trigonometry 2015-02-13T00:00:00Z The complement of the logarithm of a sine, tangent, or secant. The Sailor's Word-Book An Alphabetical Digest of Nautical Terms, including Some More Especially Military and Scientific, but Useful to Seamen; as well as Archaisms of Early Voyagers, etc. The programme will conclude with a costume ball, at which everybody present will be disguised as a different logarithm. Punch, or the London Charivari, Vol. 146, June 3, 1914 See if you can make him remember logarithms.” A Collection of Stories, Reviews and Essays About twenty years ago, I discovered this method of directly calculating logarithms. A Budget of Paradoxes, Volume II What is its relationship to a logarithm with base and how does the notation differ? Algebra and Trigonometry 2015-02-13T00:00:00Z I feel myself becoming a personification of Algebra, a living trigonometrical canon, a walking table of logarithms. Historical Essays At any rate, you will get away from the tyranny of the commonplace, the conventional, the methodical, which transforms the rhythm of life into a logarithm. Days Off And Other Digressions There are also exceptional natures that delight in mathematics, minds whose young affections run to angles and logarithms, and with whom the computation of values is itself the chief value in life. The Atlantic Monthly, Volume 18, No. 107, September, 1866 I could generally find the logarithm of any number in a minute or two without the use of books or tables. A Budget of Paradoxes, Volume II For the following exercises, use the definition of common and natural logarithms to simplify. Algebra and Trigonometry 2015-02-13T00:00:00Z In the year 1624 Mr Gunter, professor of astronomy at Gresham College, Cambridge, published his scale of logarithms, sines, etcetera, and invented the scale which has since gone by his name. How Britannia Came to Rule the Waves Updated to 1900 Argoli's discovery that logarithms facilitate easy processes, but increase the labor of difficult ones, is worth recording. A Budget of Paradoxes, Volume I This, however, has been the fate of many inventions, as witness our neglect of logarithms and of contracted processes to-day. The Hindu-Arabic Numerals That was short for logarithm, you know, because I was such a log at arithmetic. Adam Johnstone's Son TRY IT #11 Give the equation of the natural logarithm graphed in Figure 16. Algebra and Trigonometry 2015-02-13T00:00:00Z As Fechner states it, 'Sensation varies, not as the stimulus, but as the logarithm of the stimulus.' Mind and Motion and Monism Though they are not fact and true, or nature, but analogous to it, in the manner of the artificial numbers of logarithms, sines, &c. A Budget of Paradoxes, Volume I Later it was found more convenient to choose it equal to 2.512, the logarithm of which number has the value 0.4. Lectures on Stellar Statistics They never goes at the investigation o’ the subject as a man investigates mathematics, or navigation, or logarithms; so they’re like a ship at sea without a chart. Jarwin and Cuffy The equivalence of and is one of the logarithm properties we will examine in this section. Algebra and Trigonometry 2015-02-13T00:00:00Z There’s a proverb somewhere—” “In Milton, maybe, or Napier’s book o’ logarithms,” suggested Captain Bunting. The Golden Dream Adventures in the Far West It seems that gravitation is not truth, but only the logarithm of it. A Budget of Paradoxes, Volume I The magnitudes play the same rôle in relation to the quantities of light as do the logarithms to the corresponding numbers. Lectures on Stellar Statistics You see, I regard the Bible as my class-book, my book o’ logarithms, chart compass, rudder, etcetera, all rolled into one. The Young Trawler Some important properties of logarithms are given here. Algebra and Trigonometry 2015-02-13T00:00:00Z So now I’m drawing circles and triangles at every available moment, and my logarithm tables are thumbed almost to death. The Adventures of a Three-Guinea Watch From astronomy and chronology he was drawn into the study of mathematics, and the logarithms in the tables of Collet. Memoir of the Life of John Quincy Adams. The magnitudes being themselves logarithms of a kind, it is evidently more convenient to use a simple value of the logarithm of the ratio of intensity than to use this ratio itself. Lectures on Stellar Statistics I had conjured up the fantasy of a system which would contain the whole of life, be as reliable as a table of logarithms, foresee all possible emergencies and offer entirely trustworthy rules of action. A Preface to Politics In these cases, we solve by taking the logarithm of each side. Algebra and Trigonometry 2015-02-13T00:00:00Z It contains at the back of the slide scales for the logarithms of sines and tangents so arranged that they can be worked with the scale on the front. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" During these conferences the alteration proposed by Briggs was agreed upon; and on his return from his second visit to Edinburgh in 1617 he accordingly published the first chiliad of his logarithms. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 3 "Brescia" to "Bulgaria" Seated at the same table as herself was a skilful sailor, using logarithms, secants and cosecants, polar distances and hour angles, as if he were in some university class-room. The Captain of the Kansas I once told him that his method of argument was to that of ordinary lawyers like logarithms to ordinary mathematics. Autobiography of Seventy Years, Vol. 1-2 Recall, since is equivalent to we may apply logarithms with the same base on both sides of an exponential equation. Algebra and Trigonometry 2015-02-13T00:00:00Z They are almost as old as logarithms themselves. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" Only thing is, I'll have to work up the logarithms by hand, instead of using the computer. Stand by for Mars! Our comrade of the illustrious navy of the United States of America has only one explanation for everything: his Japanese logarithms, by means of which he figures out everything. Banzai! by Parabellum He was not so much hostile to beauty as devoid of any consciousness of it; he stood as unmoved before its phenomena as a savage before a table of logarithms. A Book of Prefaces One such situation arises in solving when the logarithm is taken on both sides of the equation. Algebra and Trigonometry 2015-02-13T00:00:00Z I always thought you were a sort of calculating machine, who slept on a logarithm table. The Man Who Rocked the Earth "If you would write a code, or logarithms, or a cook-book, you cannot spare the poetic impulse." The Last Harvest It is psychological, of course, and it is not hard to explain simply in terms of human experience plus the known fact that the human senses respond to the logarithm of the stimulus. The Fourth R His father was distressed, and sought by bribes to get him to quit scrawling with pencil and turn his attention to logarithms and other useful things; but with only partial success. Little Journeys to the Homes of the Great - Volume 04 Little Journeys to the Homes of Eminent Painters In such cases, remember that the argument of the logarithm must be positive. Algebra and Trigonometry 2015-02-13T00:00:00Z Happy evenings could then be spent with a book of logarithms and sheets of paper specially cut to accommodate a problem. The Spinster Book But suppose you should talk of surds, simple and quadratic equations, diophantine problems, and logarithms, to a person who knows nothing of proportion or relation, addition or subtraction. Lectures on Language As Particularly Connected with English Grammar. The engineer, on the other hand, is a man of brass and iron and logarithms; in imagination he is blind, in flexibility he resembles reinforced concrete. The Navy as a Fighting Machine Next to geometry and logarithms and the Bible, the best discipline preparatory to making you a lawyer is the translation of Latin. The Young Man and the World If the number we are evaluating in a logarithm function is negative, there is no output. Algebra and Trigonometry 2015-02-13T00:00:00Z Papers littered the floor; bundles of manuscripts, lists, charts, and observations, the worn and battered tin box of records, note-books, journals, tables of logarithms were piled upon Bennett's desk. A Man's Woman Fortunately, he had made up for this in his oral examination with his logarithms, geometry, and history of architecture, for he was very strong in the scientific parts. His Masterpiece I think that while Christ would not have understood Frederick Taylor's technique, his tables of figures or foot-tons or logarithms he would have understood Frederick Taylor. Crowds A Moving-Picture of Democracy There is no such remorseless logic as that of logarithms. The Young Man and the World Therefore, when given an equation with logs of the same base on each side, we can use rules of logarithms to rewrite each side as a single logarithm. Algebra and Trigonometry 2015-02-13T00:00:00Z "Now, Mr. Scott, don't open Bowditch's Navigator to us, or talk about projection,' 'logarithms,' 'Gunter,' and 'inspection;' for I am not capable of understanding them, for my trigonometry has gone to the weeping willows." Across India Or, Live Boys in the Far East They have only to apply sines and co-sines, tangents and logarithms to a stock exchange quotation for me to grovel before their superior wisdom and consult them at every turn in life. Mrs. Warren's Daughter A Story of the Woman's Movement To tell the truth, if it were not for those beastly logarithms, the Duke was no mean sailing-master himself, and he knew a seaman when he saw one; hence his remark about Claudius. Doctor Claudius, A True Story Very early he put his knowledge of the surveyor's art to practical test, and applied the chain and logarithm to the reaches of the family lands. Washington's Birthday We have used exponents to solve logarithmic equations and logarithms to solve exponential equations. Algebra and Trigonometry 2015-02-13T00:00:00Z He wasn't even trained, as the rest of us understood training; and he scoffed at the drawing-office, and laughed outright at logarithms and our laborious methods of getting out quantities. Widdershins He was still in the toils of the might-have-been, of that wasting process—an examination, and turning over in his mind logistics, logarithms, trajectories, equations, and a mob of disconnected questions. Westways The slightest deviation from established custom seems to act on the people at the restaurant like a wrong figure in a table of logarithms. Lippincott's Magazine of Popular Literature and Science Volume 12, No. 30, September, 1873 In July, while at work on logarithm tables, he was overtaken by a sudden fainting fit, evidently of an epileptic nature. Shandygaff We are now ready to combine our skills to solve equations that model real-world situations, whether the unknown is in an exponent or in the argument of a logarithm. Algebra and Trigonometry 2015-02-13T00:00:00Z "Put your watch ahead one hour, and then go through the same logarithms you always do." Mince Pie The most effective tools of the mathematician are framed from the Arab algebra and Napier's logarithms. Lippincott's Magazine of Popular Literature and Science Volume 17, No. 097, January, 1876 I have often wondered who worked out the table of logarithms, and have thought how much more agreeable life has been for many people because of his work. Reveries of a Schoolmaster In the first term algebra, logarithms and geometry had to be finished, for in the second term trigonometry was the subject in mathematics. Dave Darrin's First Year at Annapolis For the following exercises, use the definition of a logarithm to rewrite the equation as an exponential equation. Algebra and Trigonometry 2015-02-13T00:00:00Z The title page was missing, but its contents were chiefly tables of logarithms. Lander's Travels The Travels of Richard Lander into the Interior of Africa The title-page was missing, but its contents were chiefly tables of logarithms. The Mirror of Literature, Amusement, and Instruction Volume 19, No. 542, April 14, 1832 Napier’s invention of logarithms at once attracted Kepler’s attention. Kepler In mathematics the new man had to recite in algebra, logarithms and geometry. Dave Darrin's First Year at Annapolis For the following exercises, use the definition of a logarithm to solve the equation. Algebra and Trigonometry 2015-02-13T00:00:00Z A Course in the slide rule and logarithms. U.S. Copyright Renewals, 1977 July - December The grave gentlemen of the tribunal had made him turn pale and stutter like a child before the logarithms and formulas of trigonometry. Mare Nostrum (Our Sea) A Novel One day, when Charles was a very small boy, he came up to his father and showed him a book of logarithms, with the request, "Please explain." The Life and Letters of Lewis Carroll (Rev. C. L. Dodgson) In every man of the seventy the sage saw the logarithm of a possible La Place, of a Sturm, or of a Newton. Stories by American Authors, Volume 5 For the following exercises, use the one-to-one property of logarithms to solve. Algebra and Trigonometry 2015-02-13T00:00:00Z A monotonously uniform exercise may by practice give great skill in one special act; but the skill is limited to that act, be it bookkeeping or calculations in logarithms or experiments in hydrocarbons. Democracy and Education: an introduction to the philosophy of education It is quite true that much of the teaching done by these early professors would sound absurd to our ears, trained to listen to logarithms and geometrical theorems. The Story of Mankind They are getting the education in the humanities the world needs more than tables of logarithms. The University of Hard Knocks People who studied the logarithms of the diapason would not be apt to think a man crazy for such a little thing as that. The Magic Egg and Other Stories For the following exercises, solve each equation by rewriting the exponential expression using the indicated logarithm. Algebra and Trigonometry 2015-02-13T00:00:00Z A savant spends two years in calculating a table of logarithms to nine or ten decimals. What is Property? But I can work out the latitude and the longitude, and I can handle my sextant and manage my logarithms. The Captain of the Polestar In trigonometry the Professor and I had a disagreement touching a little matter of logarithms. Daddy-Long-Legs One afternoon they came in together, having met on their way to the library, and entered into a conversation on diapasonic logarithms, which continued during the lady's stay in the shop. The Magic Egg and Other Stories Recall the formula for continually compounding interest, Use the definition of a logarithm along with properties of logarithms to solve the formula for time such that is equal to a single logarithm. Algebra and Trigonometry 2015-02-13T00:00:00Z On the other hand, his intelligence was no such perfected instrument as Hicks's, as exact as logarithms, as penetrating as a scalpel, as uncoloured by emotions as a steel trap. A Deal in Wheat and Other Stories of the New and Old West The man keeps a good log; works out his case like a sailing master; and proves it by alphabetic signs and logarithms, as clear as a problem in plain sailing. Jack in the Forecastle or, Incidents in the Early Life of Hawser Martingale It consisted chiefly of tables of logarithms, and between the leaves were a few loose papers of very little consequence. Life and Travels of Mungo Park in Central Africa Yet God has computed instantaneously every table of logarithms, and every other mathematical table,--no matter how difficult. The Evolution of Man Scientifically Disproved In 50 Arguments Use the definition of a logarithm along with properties of logarithms to solve the formula for time such that is equal to a single logarithm. Algebra and Trigonometry 2015-02-13T00:00:00Z It seemed to him like something divine, unheard of—like the science which taught the table of logarithms. Dame Care This motion is very interesting, for the cart pulls the pointer and the pointer directs the cart, and between they calculate a table of Naperian logarithms. Scientific American Supplement, No. 288, July 9, 1881 They also discovered a tohe or cloak, a cutlass, a double-barrelled gun, a book of logarithms, and an invitation-card, which had belonged to Park. Life and Travels of Mungo Park in Central Africa The practical application of this process of reasoning was enormously facilitated by the invention of logarithms by Napier. History of Astronomy Note that repeated applications of the product rule for logarithms allow us to simplify the logarithm of the product of any number of factors. Algebra and Trigonometry 2015-02-13T00:00:00Z Well, my poor girl, you needn't study Greek and archaeology and logarithms unless you feel inclined. Fan : the story of a young girl's life That is so true that this code is in its last analysis but a table of criminal logarithms for figuring out penalties. The Positive School of Criminology Three Lectures Given at the University of Naples, Italy on April 22, 23 and 24, 1901 What an infinity of calculation, in the infancy of science,--before the invention of logarithms,--was necessary to arrive at these truths! Beacon Lights of History, Volume 06 Renaissance and Reformation Instinctively he took the nearest thing to his hand, a book of logarithms, and flung it at it. Dracula's Guest For example, consider Using the product rule for logarithms, we can rewrite this logarithm of a product as the sum of logarithms of its factors: Algebra and Trigonometry 2015-02-13T00:00:00Z Books are a source both of instruction and of amusement; a table of logarithms is a book; therefore it is a source both of instruction and of amusement. Practical Argumentation I'm getting a bit too old and stiff for it nowadays, sir—just scratch about in the garden here and grow a bit of a logarithm, or raise a common denominator or two. Literary Lapses The table of logarithms is one thing, and its vital play, in botany, music, optics, and architecture, another. Representative Men Let us forget, this happy evening, that there are such things as logarithms, and sines, and tangents, and Greek tragedies. Walter Sherwood's Probation Next we write the equivalent equation by summing the logarithms of each factor. Algebra and Trigonometry 2015-02-13T00:00:00Z I've been trying to keep up my Greek, and then I do believe there's some way of simplifying those accounts by logarithms, if I could but work it out. The Young Step-Mother He would spend half a day in these preparations without ever working out a problem or having the faintest conception of the use of lines or logarithms. The Gilded Age, Part 2. In reading logarithms, one is not more secure, than in following Plato in his flights. Representative Men I have expressly requested Mr. Daniels to provide no logarithms to- night. Walter Sherwood's Probation Notice that the resulting terms are logarithms of products. Algebra and Trigonometry 2015-02-13T00:00:00Z But when the mental prevailed, then there was an entrancing five minutes' digging among out-of-date almanacs, volumes of Scotch theology, and tables of logarithms, until one found something which made it all worth while. Through the Magic Door I never found that people who were learned in logarithms and other kinds of poetry were any quicker in washing dishes or darning socks. Parnassus on Wheels It is AS IF they existed; but in reality they are like co-ordinates or logarithms, only artificial short-cuts for taking us from one part to another of experience's flux. Pragmatism Oh! my gentleman's below, brushing up his logarithms. Jack Tier Notice that we used the product rule for logarithms to find a solution for the example above. Algebra and Trigonometry 2015-02-13T00:00:00Z Time was I thought I could never work out a logarithm without a formula, but I mastered that. Love Me Little, Love Me Long "That will come," said Jim, "the day after Sam has got the right to look after Alice; not before; the governor is too fond of his logarithms." Recollections of Geoffrey Hamlyn Amongst other inconveniences the piece also contains logarithms, to which the respectable German Philistine cannot attain. Letters of Franz Liszt -- Volume 1 from Paris to Rome: Years of Travel as a Virtuoso She fidgeted, till Mr. Ernescliffe asked Norman if there was a table of logarithms in the house. The Daisy chain, or Aspirations Keep in mind that, although the input to a logarithm may not be written as a power, we may be able to change it to a power. Algebra and Trigonometry 2015-02-13T00:00:00Z The provoking part of it was that the Dean knew perfectly well that with the help of logarithms he could have done the thing in a moment. Sunshine Sketches of a Little Town The pedigrees of our county families, arranged in diagrams on the pages of county histories, mostly appear at first sight to be as barren of any touch of nature as a table of logarithms. A Group of Noble Dames One whole afternoon I sat in the cockpit, steering with one hand and studying logarithms with the other. The Cruise of the Snark He was conscious of nothing but his book; however, she found the logarithms, and brought them to Mr. Ernescliffe, staying to look at his drawing, and asking what he was making out. The Daisy chain, or Aspirations For the expression we identify the factor, 4, as the exponent and the argument, as the base, and rewrite the product as a logarithm of a power: Algebra and Trigonometry 2015-02-13T00:00:00Z Bidder, for instance, declares that it is impossible for him to say how he can instinctively tell the logarithm of a number consisting of seven or eight figures. The Unknown Guest Mathematicians find his computation peculiarly interesting because it evidences a crude conception of the idea of logarithms. A History of Science — Volume 1 Haliburton, not strong in spherical trigonometry, looked out logarithms for me till breakfast, and, as soon as it would do, went over to Mrs. Bowdoin, to borrow her telescope, ours being left at No. 9. The Brick Moon and Other Stories What an infinity of calculation, in the infancy of science—before the invention of logarithms,—was necessary to arrive at these truths! Beacon Lights of History TRY IT #5 Rewrite using the power rule for logs to a single logarithm with a leading coefficient of 1. Algebra and Trigonometry 2015-02-13T00:00:00Z The wrong logarithm was taken, and of course that threw out all the calculations. Tom Swift and His Undersea Search, or, the Treasure on the Floor of the Atlantic We will learn later how to change the base of any logarithm before condensing. Algebra and Trigonometry 2015-02-13T00:00:00Z TRY IT #10 Rewrite as a single logarithm. Algebra and Trigonometry 2015-02-13T00:00:00Z To derive the change-of-base formula, we use the one-to-one property and power rule for logarithms. Algebra and Trigonometry 2015-02-13T00:00:00Z We can also apply the product rule to express a sum or difference of logarithms as the logarithm of a product. Algebra and Trigonometry 2015-02-13T00:00:00Z TRY IT #13 Change to a quotient of natural logarithms. Algebra and Trigonometry 2015-02-13T00:00:00Z Q&A Can we change common logarithms to natural logarithms? Algebra and Trigonometry 2015-02-13T00:00:00Z For the following exercises, expand each logarithm as much as possible. Algebra and Trigonometry 2015-02-13T00:00:00Z For the following exercises, condense to a single logarithm if possible. Algebra and Trigonometry 2015-02-13T00:00:00Z It is important to remember that the logarithms must have the same base to be combined. Algebra and Trigonometry 2015-02-13T00:00:00Z For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Algebra and Trigonometry 2015-02-13T00:00:00Z For the following exercises, use properties of logarithms to evaluate without using a calculator. Algebra and Trigonometry 2015-02-13T00:00:00Z |
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