| 单词 | logarithmic |
| 例句 | Nat laid aside Moore, and spread the logarithmic tables he was making. Carry On, Mr. Bowditch 1955-01-01T00:00:00Z He read books on calculus and logarithmic algebra and loved what he called the poetry and symmetry of math. The Glass Castle 2005-03-01T00:00:00Z “If we had logarithmic tables of all the trigometric functions, you could work any problem in navigation with nothing but addition and subtraction.” Carry On, Mr. Bowditch 1955-01-01T00:00:00Z 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 virtue of such a coarse logarithmic safety scale is that it provides us, and particularly the media, with an order-of-magnitude estimate of the risks associated with various activities, illnesses, and procedures. Innumeracy: Mathematical Illiteracy and Its Consequences 1988-01-01T00:00:00Z The logarithmic system ensures you’re not matched with someone who just happened to share lots of trivial things in common with you but was miles away on the important stuff. You are more than a sexual fetish — but online dating sites might not think so 2014-03-15T20:30:00Z These are exponential times, and we are a logarithmic people. America slouches into a new pandemic year 2021-12-29T05:00:00Z The point value is logarithmic so the values increase exponentially as opposed to linearly. You are more than a sexual fetish — but online dating sites might not think so 2014-03-15T20:30:00Z The pH scale is logarithmic, so each whole number signals a value 10 times different from the number above or below. Dull Caesarstone? Try this to restore the shine. 2019-04-19T04:00:00Z The scale for brightness is reverse logarithmic, which means the brighter an object is, the lower its magnitude number. Newly discovered comet arriving in 2024 could be brighter than Venus 2023-03-10T05:00:00Z The scale’s objective, base-10 logarithmic system caught on, and although it’s been superseded, people still attach his name to the scale. How the deadly Long Beach earthquake in 1933 propelled California's seismic safety rules 2023-03-07T05:00:00Z But the February 6 earthquake was a 7.8—about four times bigger on the logarithmic scale of earthquake magnitudes. How to Engineer Buildings That Withstand Earthquakes 2023-02-22T05:00:00Z Earthquakes are measured on a logarithmic scale, which means the difference between a 6.8 and a 7.8 is bigger than it sounds. Was the earthquake’s high death toll preventable? Geologists say yes. 2023-02-09T05:00:00Z It is a logarithmic scale: For each whole-number it rises, the amount of energy released by an earthquake increases by about 32 times. How strong is a magnitude-7.8 quake? 2023-02-06T05:00:00Z Her goal for the acceleration days was straightforward: Begin to improve her grade in the yearlong course and master logarithmic functions. L.A. students and their parents to get unique roadmap to improve academic weaknesses 2022-12-21T05:00:00Z Figure 13.8 Each increment on this logarithmic scale indicates an increase by a factor of ten, and thus illustrates the tremendous range of temperatures in nature. College Physics for AP Courses 2015-08-12T00:00:00Z The pH provided is a logarithmic measure of the hydronium ion concentration resulting from the acid ionization of the nitrous acid, and so it represents an “equilibrium” value for the ICE table: Chemistry 2019-02-14T00:00:00Z The “e” in the formula is a constant with the approximate value of 2.71828 and is the base of the natural logarithmic exponential growth formula. Introductory Business Statistics 2017-11-29T00:00:00Z We can solve and evaluate logarithmic equations by using the technique of converting the equation to its equivalent exponential form. College Algebra with Corequisite Support 2020-09-23T00:00:00Z No. A horizontal asymptote would suggest a limit on the range, and the range of any logarithmic function in general form is all real numbers. College Algebra 2021-12-21T00:00:00Z Note that zero on a logarithmic scale would occur off the bottom of the page at infinity. College Physics for AP Courses 2015-08-12T00:00:00Z This equation is often rearranged into logarithmic form to yield the linear equation: Chemistry 2019-02-14T00:00:00Z Double logarithmic transformation of the data will provide an easy way to test this particular shape of the relationship. Introductory Business Statistics 2017-11-29T00:00:00Z To graph a logarithmic function , it is easiest to convert the equation to its exponential form, . College Algebra with Corequisite Support 2020-09-23T00:00:00Z Recall that the argument of a logarithmic function must be positive, so we determine where . College Algebra 2021-12-21T00:00:00Z This will often be the method to solve some exponential and logarithmic equations. Intermediate Algebra 2020-05-06T00:00:00Z The pressure axis is plotted on a logarithmic scale to accommodate the large range of values. Chemistry 2019-02-14T00:00:00Z By elementary function, we mean a function that can be written using a finite number of algebraic combinations or compositions of exponential, logarithmic, trigonometric, or power functions. Calculus, Vol 2 2016-03-30T00:00:00Z There are two types of logarithmic equations: those with log terms on just one side of the equation or those with log terms on each side of the equation. College Algebra with Corequisite Support 2020-09-23T00:00:00Z It is also an approximate position on a logarithmic scale; Sample response: Orders of magnitude are useful when making comparisons between numbers that differ by a great amount. College Algebra 2021-12-21T00:00:00Z Some growth is described by the types of functions you will explore in this chapter—exponential and logarithmic. Intermediate Algebra 2020-05-06T00:00:00Z A common means of expressing quantities that may span many orders of magnitude is to use a logarithmic scale. Chemistry 2019-02-14T00:00:00Z For example, if an integral contains a logarithmic function and an algebraic function, we should choose u to be the logarithmic function, because L comes before A in LIATE. Calculus, Vol 2 2016-03-30T00:00:00Z Since the domain of logarithmic functions is positive numbers only, make sure to check the solutions. College Algebra with Corequisite Support 2020-09-23T00:00:00Z We define polynomial, rational, trigonometric, exponential, and logarithmic functions. Calculus, Volume 1 2016-03-30T00:00:00Z In this chapter, we will introduce two new types of functions, exponential functions and logarithmic functions. Intermediate Algebra 2020-05-06T00:00:00Z We can use the power rule to expand logarithmic expressions involving negative and fractional exponents. Algebra and Trigonometry 2015-02-13T00:00:00Z Since we do not have integration formulas that allow us to integrate simple logarithmic functions and inverse trigonometric functions, it makes sense that they should not be chosen as values for dv. Calculus, Vol 2 2016-03-30T00:00:00Z Use the one-to-one property of logarithmic equality to set arguments equal to one another. College Algebra with Corequisite Support 2020-09-23T00:00:00Z The most common transcendental functions are trigonometric, exponential, and logarithmic functions. Calculus, Volume 1 2016-03-30T00:00:00Z In the next example we do the reverse—convert logarithmic form to exponential form. Intermediate Algebra 2020-05-06T00:00:00Z With practice, we can look at a logarithmic expression and expand it mentally, writing the final answer. Algebra and Trigonometry 2015-02-13T00:00:00Z Another type of spiral is the logarithmic spiral, described by the function r = a · bθ. Calculus, Vol 2 2016-03-30T00:00:00Z Objective 1: Convert between exponential and logarithmic form. College Algebra with Corequisite Support 2020-09-23T00:00:00Z In this section we examine exponential and logarithmic functions. Calculus, Volume 1 2016-03-30T00:00:00Z The magnitude R of an earthquake is measured by a logarithmic scale called the Richter scale. Intermediate Algebra 2020-05-06T00:00:00Z Use the definition of a logarithm to solve logarithmic equations. Algebra and Trigonometry 2015-02-13T00:00:00Z Seismographs measure the energy released by an earthquake using a logarithmic scale of magnitude units; the Moment Magnitude Scale has replaced the original Richter Scale. An Introduction to Geology 2017-01-01T00:00:00Z Do the graphs of , , and have the shape we expect from a logarithmic function where ? College Algebra with Corequisite Support 2020-09-23T00:00:00Z We use the properties of these functions to solve equations involving exponential or logarithmic terms, and we study the meaning and importance of the number e. Calculus, Volume 1 2016-03-30T00:00:00Z In the following exercises, convert each logarithmic equation to exponential form. Intermediate Algebra 2020-05-06T00:00:00Z Use the one-to-one property of logarithms to solve logarithmic equations. Algebra and Trigonometry 2015-02-13T00:00:00Z The Richter Scale is logarithmic, based on powers of 10. An Introduction to Geology 2017-01-01T00:00:00Z The family of logarithmic functions includes the parent function along with all its transformations: shifts, stretches, compressions, and reflections. College Algebra with Corequisite Support 2020-09-23T00:00:00Z We also define hyperbolic and inverse hyperbolic functions, which involve combinations of exponential and logarithmic functions. Calculus, Volume 1 2016-03-30T00:00:00Z Explain how to change an equation from logarithmic form to exponential form. Intermediate Algebra 2020-05-06T00:00:00Z Solve applied problems involving exponential and logarithmic equations. Algebra and Trigonometry 2015-02-13T00:00:00Z Like the Richter Scale, the moment magnitude scale is logarithmic. An Introduction to Geology 2017-01-01T00:00:00Z The base of a logarithmic function must be positive, so we eliminate . College Algebra with Corequisite Support 2020-09-23T00:00:00Z Although Euler did not discover the number, he showed many important connections between e and logarithmic functions. Calculus, Volume 1 2016-03-30T00:00:00Z Now that we have the properties we can use them to “expand” a logarithmic expression. Intermediate Algebra 2020-05-06T00:00:00Z We can express the relationship between logarithmic form and its corresponding exponential form as follows: Algebra and Trigonometry 2015-02-13T00:00:00Z He plotted on logarithmic paper every trade involving a draft pick over the previous four years. The enduring value of the NFL draft’s most famous and misunderstood chart 2022-04-25T04:00:00Z TRY IT #15 Use a graphing calculator to estimate the approximate solution to the logarithmic equation to 2 decimal places. College Algebra with Corequisite Support 2020-09-23T00:00:00Z Therefore, it has an inverse function, called the logarithmic function with base b. Calculus, Volume 1 2016-03-30T00:00:00Z When we have a radical in the logarithmic expression, it is helpful to first write its radicand as a rational exponent. Intermediate Algebra 2020-05-06T00:00:00Z TRY IT #1 Write the following logarithmic equations in exponential form. Algebra and Trigonometry 2015-02-13T00:00:00Z That isn’t how it is, though, because the moment magnitude scale is logarithmic. A deadly earthquake absolutely, positively will ravage Seattle at some point. Here’s how to survive it. 2022-04-01T04:00:00Z The magnitude of an earthquake is measured by a logarithmic scale called the Richter scale. College Algebra with Corequisite Support 2020-09-23T00:00:00Z The most commonly used logarithmic function is the function loge. Calculus, Volume 1 2016-03-30T00:00:00Z 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 TRY IT #2 Write the following exponential equations in logarithmic form. Algebra and Trigonometry 2015-02-13T00:00:00Z “I think in the upcoming weeks we will have a logarithmic rise in requests,” he says. Western nations cut ties with Russian science, even as some projects try to remain neutral 2022-03-07T05:00:00Z Though the quake in 2010 measured 7.0, the Richter scale is logarithmic, meaning that Saturday’s earthquake released twice as much energy as the previous one. Explainer: Why does Haiti have earthquakes? 2021-08-16T04:00:00Z 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 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 For the following exercises, evaluate the base logarithmic expression without using a calculator. Algebra and Trigonometry 2015-02-13T00:00:00Z But by tracking and analyzing the mileage, they noticed that a sheet never stopped forming creases, although it did so at a logarithmic rate, adding fewer creases with each recrumpling. The Latest Wrinkle in Crumple Theory 2021-03-08T05:00:00Z In other words, the virus' logarithmic spread works both ways: possible exponential growth but also possible exponential reduction. 90% of US COVID-19 deaths may have been prevented if social distancing began sooner: epidemiologists 2020-04-17T04:00:00Z Using this change of base, we typically write a given exponential or logarithmic function in terms of the natural exponential and natural logarithmic functions. Calculus, Volume 1 2016-03-30T00:00:00Z Notice the x-axis is the horizontal asymptote for the exponential functions and the y-axis is the vertical asymptote for the logarithmic functions. Intermediate Algebra 2020-05-06T00:00:00Z For the following exercises, evaluate the common logarithmic expression without using a calculator. Algebra and Trigonometry 2015-02-13T00:00:00Z It marks not just the absolute growth of cases, but the rate at which cases are doubling, helping readers gauge whether an outbreak is slowing down. 91-DIVOC also helps demonstrate the value of logarithmic charts. The best graphs and data for tracking the coronavirus pandemic 2020-04-02T04:00:00Z “The biggest issue right now is we need to plan for a logarithmic increase in patient numbers,” Dr. Jason Persoff, assistant director of emergency preparedness at UCHealth, Colorado’s largest health system. U.S. hospitals say coronavirus school closures add to staffing pressure 2020-03-14T04:00:00Z Since the hyperbolic functions themselves involve exponential functions, the inverse hyperbolic functions involve logarithmic functions. Calculus, Volume 1 2016-03-30T00:00:00Z Just as e was a base for an exponential function, it can be used a base for logarithmic functions too. Intermediate Algebra 2020-05-06T00:00:00Z Figure 1 shows this point on the logarithmic graph. Algebra and Trigonometry 2015-02-13T00:00:00Z The researchers think solid obstacles, cut with small notches and arrayed in a logarithmic spiral, may be able to protect miners in the event of an underground explosion. Cannibalistic Cancer, Protection from “Blast Belly” and Chicken Inner Space: Science GIFs to Start Your Week 2019-09-30T04:00:00Z Considering the decibel scale is logarithmic, not linear, that difference is pretty huge. Mario Andretti has a hilarious take on making electric cars louder 2019-05-06T04:00:00Z The pH of a substance is defined by the logarithmic function pH = −log⎡H+ ⎤. Calculus, Volume 1 2016-03-30T00:00:00Z The logarithmic function with base e is called the natural logarithmic function. Intermediate Algebra 2020-05-06T00:00:00Z The range, as with all general logarithmic functions, is all real numbers. Algebra and Trigonometry 2015-02-13T00:00:00Z The FCC auction, however, would allow –20 dBW of noise, a significantly higher level, especially given its measure on a logarithmic scale. Lawmakers seek delay of radio spectrum auction for next-gen cell service, saying 5G plans could hurt weather satellite data 2019-03-13T04:00:00Z Astronomers rank how bright an object shines in our sky on a logarithmic scale. Back-to-back fireballs bolted through Washington’s sky Monday evening 2018-12-11T05:00:00Z Trigonometric, exponential, and logarithmic functions are examples of transcendental functions. Calculus, Volume 1 2016-03-30T00:00:00Z 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 The inverse of every logarithmic function is an exponential function and vice-versa. Algebra and Trigonometry 2015-02-13T00:00:00Z At another point, Judge Alsup and Allen went on a long, wandering detour about whether the relationship between two variables was logarithmic or linear. Chevron’s lawyer, speaking for major oil companies, says climate change is real and it’s your fault 2018-03-22T04:00:00Z The logarithmic nature of the earthquake-magnitude scale, though, means the third of these is 1,000 times more powerful than the first. Finding more time to detect a tsunami 2018-02-22T05:00:00Z The natural exponential function is y = ex and the natural logarithmic function is y = ln x = loge x. Calculus, Volume 1 2016-03-30T00:00:00Z To solve logarithmic equations, one strategy is to change the equation to exponential form and then solve the exponential equation as we did before. Intermediate Algebra 2020-05-06T00:00:00Z For the following exercises, write a logarithmic equation corresponding to the graph shown. Algebra and Trigonometry 2015-02-13T00:00:00Z My doctor warned me that the pain wouldn't double with every loss, that it would be logarithmic--the curve getting ever steeper. When You're Pregnant, Everyone Is Suddenly an 'Expert' on Your Health 0002-11-29T05:00:00Z The shift might seem slight, but it actually represents a 30 percent increase in acidity, because the pH scale is logarithmic. Chesapeake acidification may compound issues already facing bay, researchers find 2017-10-11T04:00:00Z Given an exponential function or logarithmic function in base a, we can make a change of base to convert this function to any base b > 0, b ≠ 1. Calculus, Volume 1 2016-03-30T00:00:00Z As we solve logarithmic equations, y = loga x , we need to remember that for the base a, a > 0 and a ≠ 1. Intermediate Algebra 2020-05-06T00:00:00Z TRY IT #11 Use a graphing calculator to estimate the approximate solution to the logarithmic equation to 2 decimal places. Algebra and Trigonometry 2015-02-13T00:00:00Z Because pH is measured on a logarithmic scale, every change of 0.1 units results in a 26% increase in concentration of hydrogen ions. Sea change : Nature : Nature Research 2017-10-10T04:00:00Z Percentages of mutagenic indels on the x-axis are presented on a logarithmic scale. Correction of a pathogenic gene mutation in human embryos : Nature : Nature Research 2017-08-01T04:00:00Z In this section, we explore derivatives of exponential and logarithmic functions. Calculus, Volume 1 2016-03-30T00:00:00Z These will be very helpful as we continue to solve both exponential and logarithmic equations. Intermediate Algebra 2020-05-06T00:00:00Z We have seen that any exponential function can be written as a logarithmic function and vice versa. Algebra and Trigonometry 2015-02-13T00:00:00Z Because joystick deflection increased sound frequency exponentially, we used a logarithmic scale and measured frequency in octaves relative to the starting frequency of 2 kHz. Mapping of a non-spatial dimension by the hippocampal–entorhinal circuit : Nature : Nature Research 2017-03-28T04:00:00Z Percentages of mutagenic indels on the x-axis are presented on a logarithmic scale. Correction of a pathogenic gene mutation in human embryos : Nature : Nature Research 2017-08-01T04:00:00Z Use logarithmic differentiation to find the derivative of y = xx. Calculus, Volume 1 2016-03-30T00:00:00Z In the following exercises, convert each logarithmic equation to exponential form. Intermediate Algebra 2020-05-06T00:00:00Z We will concentrate on three types of regression models in this section: exponential, logarithmic, and logistic. Algebra and Trigonometry 2015-02-13T00:00:00Z They continued deflecting the joystick to increase the frequency along a perceptually uniform logarithmic axis22. Mapping of a non-spatial dimension by the hippocampal–entorhinal circuit : Nature : Nature Research 2017-03-28T04:00:00Z Scale bar, 10 μm. d, Cumulative histogram of distances between the centroids of all pairs of cells detected within the same imaging session, plotted with a logarithmic scale. Neural ensemble dynamics underlying a long-term associative memory : Nature : Nature Research 2017-03-21T04:00:00Z Next we see how to use L’Hôpital’s rule to compare the growth rates of power, exponential, and logarithmic functions. Calculus, Volume 1 2016-03-30T00:00:00Z Convert the equation from exponential to logarithmic form: 10−2 = 1 . Intermediate Algebra 2020-05-06T00:00:00Z As with exponential models, data modeled by logarithmic functions are either always increasing or always decreasing as time moves forward. Algebra and Trigonometry 2015-02-13T00:00:00Z The decibel scale is logarithmic, rather than linear, so a difference of a few decibels is important. Analysis | Are firearms with a silencer ‘quiet’? 2017-03-20T04:00:00Z Scale bar, 10 μm. d, Cumulative histogram of distances between the centroids of all pairs of cells detected within the same imaging session, plotted with a logarithmic scale. Neural ensemble dynamics underlying a long-term associative memory : Nature : Nature Research 2017-03-21T04:00:00Z Figure 4.74 A power function grows at a faster rate than a logarithmic function. Calculus, Volume 1 2016-03-30T00:00:00Z The next two properties can also be verified by converting them from exponential form to logarithmic form, or the reverse. Intermediate Algebra 2020-05-06T00:00:00Z Recall that logarithmic functions increase or decrease rapidly at first, but then steadily slow as time moves on. Algebra and Trigonometry 2015-02-13T00:00:00Z Charles Richter's eponymous, logarithmic scale of earthquake classification made him globally famous. New in paperback : Nature : Nature Research 2016-10-04T04:00:00Z There are two types of redshift: Doppler and cosmological, this is the latter - it’s a logarithmic distance scale based on the expansion of the universe. Week in Geek: A galaxy far, far away edition 2016-03-06T05:00:00Z Exponential and logarithmic functions are used to model population growth, cell growth, and financial growth, as well as depreciation, radioactive decay, and resource consumption, to name only a few applications. Calculus, Volume 1 2016-03-30T00:00:00Z The logarithmic equation loga ax = x converts to the exponential equation ax = ax, which is also a true statement. Intermediate Algebra 2020-05-06T00:00:00Z Use logarithmic regression to fit a model to these data. Algebra and Trigonometry 2015-02-13T00:00:00Z That's because the earthquake scale—called the Moment Magnitude Scale, which replaced the Richter Scale—is logarithmic, rather than arithmetic. What Earthquake Maps Should Really Look Like 2015-10-03T04:00:00Z Spirals like the ones found within the chambered nautilus form a shape known as a logarithmic spiral, in which the gaps between each whorl are spaced incrementally farther apart in a precise mathematical manner. The vast and complicated universe inside a seashell 2015-07-31T04:00:00Z In this section, we explore integration involving exponential and logarithmic functions. Calculus, Volume 1 2016-03-30T00:00:00Z Both ended up with the identity function which shows again that the exponential and logarithmic functions are inverse functions. Intermediate Algebra 2020-05-06T00:00:00Z Graph the logarithmic equation on the scatter diagram. Algebra and Trigonometry 2015-02-13T00:00:00Z Sound is measured on a logarithmic scale, so the proposed 17-decibel jump will actually be perceived by human hearing as almost four times as loud as the current limit. Clamoring for quiet 2015-05-29T04:00:00Z The magnitude scale used to measure earthquakes is deceptive; it doesn't show a steady, linear progression but a logarithmic one. Nepal earthquake: A legacy of fear in Chautara - BBC News 2015-05-14T04:00:00Z Exponential and logarithmic functions arise in many real-world applications, especially those involving growth and decay. Calculus, Volume 1 2016-03-30T00:00:00Z We know exponential functions and logarithmic function are very interrelated. Intermediate Algebra 2020-05-06T00:00:00Z Graph the logarithmic equation on the scatter diagram. Algebra and Trigonometry 2015-02-13T00:00:00Z Kimberly Noble of Columbia University in New York and her colleagues reported that the relationship between income and brain surface area was logarithmic. Children Of Rich Parents Have Bigger Brains 2015-03-31T04:00:00Z Those levels compare to a global average of 8.1 on the logarithmic pH scale, which runs from the most acidic measurement of zero to the most alkaline measurement of 14. Study: World’s most acidic sea water in Bering Sea 2014-11-22T05:00:00Z Thus, we see that all logarithmic functions are constant multiples of one another. Calculus, Volume 1 2016-03-30T00:00:00Z Whether you use Brier scores or logarithmic scores, my forecast will be judged better than yours. What the Forecasts Got Right, and Wrong 2014-11-05T05:00:00Z 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 Today it's 8.1, a 30 percent increase in acidity on the logarithmic scale. Mussels Lose Footing in More Acidic Ocean 2014-09-09T04:00:00Z Google will never tip their hat as to the actual logarithmic signals involved in a writer’s rank. What Is The True Value Of Google And Twitter Authorship? 2014-06-27T04:00:00Z Because decibels are a logarithmic scale, technically it’s possible for “95%” to be mathematically true. Are Noise Cancelling Headphones Worth It? 2014-02-21T23:25:00Z Iron content closely corresponds to what astronomers call metallicity, which is expressed on a logarithmic scale: Minus 2.0 is one-hundredth the iron abundance of the sun, –3.0 is one-thousandth, and so on. The Archaeology of the Stars 2014-02-10T22:53:32Z A graphing calculator may be used to approximate solutions to some logarithmic equations See Example 9. Algebra and Trigonometry 2015-02-13T00:00:00Z This may not sound much, but pH is a logarithmic scale. The future of the oceans: Acid test 2013-11-21T16:03:53Z Or how about this logarithmic chart: You’ll see that the recent price swings, despite being massive compared to any other mainstream currency, are quite small in proportion the over all increase, and previous price swings. Is Bitcoin Crashing As Of Early July 2013? 2013-07-12T16:56:00Z We need approaches to the solutions that aren’t just arithmetic and additive, but are in some sense logarithmic. Top Ten Quotes From Harvard's First Forum On Healthcare Innovation 2013-07-10T02:30:00Z Since the pH scale is logarithmic, this change represents a stunning 30 percent increase in acidity. How the IPCC Underestimated Climate Change 2012-12-06T17:45:00.340Z Using the general equation we can write the equation of a logarithmic function given its graph. Algebra and Trigonometry 2015-02-13T00:00:00Z We organized each unit around different types of functions: linear, piecewise, quadratic, radical, rational, exponential, logarithmic. SchoolBook: Real-World Problems + Group Learning = A.P. Calculus Success 2012-07-30T18:52:28Z The areas in which high school teachers indicated that they felt less well prepared were number bases, three-dimensional geometry, geometric transformations, logarithmic and trigonometric functions, probability, and calculus. Math Teachers Feel They're Poorly Prepared 2012-07-13T15:45:00.223Z An example appears in my post about logarithmic scales. Thinking Outside the Chart Menu: Part 2 2012-06-20T13:44:17Z 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 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 The curve is a logarithmic spiral, and the use of the instrument involves no other labor than that of setting it in position. Modern Machine-Shop Practice, Volumes I and II 2012-03-23T02:00:33.140Z There was similarly great variability in the percentage of teachers who felt that they had the coursework to make them well prepared to deal with calculus, probability, number theory, and logarithmic and trigonometric functions. Math Teachers Feel They're Poorly Prepared 2012-07-13T15:45:00.223Z The authors claim to detect a path from “preradicalization” to “jihadization,” driven by a fundamentalist ideology “proliferating in Western democracies at a logarithmic rate.” Gotham: With Muslims, Using a Brush Far Too Broad 2012-01-31T03:55:26Z Two possible ways to label a logarithmic scale with base 10 These two scales are equivalent: the top one labels the tick marks with the original values. How Should I Label Log Scales in Charts and Graphs? 2012-01-25T16:36:14Z Solve for x if by converting the logarithmic equation to exponential form. Algebra and Trigonometry 2015-02-13T00:00:00Z The common base for logarithmic scales is the base 10. When Should I Use Logarithmic Scales in My Charts and Graphs? 2012-01-19T13:02:18Z The current through this ball coherer is, therefore, a logarithmic function of the potential difference between its ends, of the form and exhibits no discontinuity. Hertzian Wave Wireless Telegraphy 2012-01-09T03:00:20.570Z Gunter’s Line, a logarithmic line, usually laid down upon scales, sectors, &c. Encyclopaedia Britannica, 11th Edition, Volume 12, Slice 6 "Groups, Theory of" to "Gwyniad" 2011-12-16T03:00:12.320Z Their first finding: good estimators possess a clear mental number line — one in which numbers are evenly spaced, or linear, rather than a logarithmic one in which numbers crowd closer together as they get bigger. Why Guessing Is Undervalued 2011-11-23T11:49:09Z Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Algebra and Trigonometry 2015-02-13T00:00:00Z The logarithmic spiral echoes the curved arms of hurricanes and distant galaxies. Too Much Love Threatens Chambered Nautilus, Scientists Say 2011-10-24T14:59:17Z Quakes are measured on a logarithmic scale, so a magnitude 9 quake has 10 times the amplitude and about 31 times more energy release than a magnitude 8, according to the U.S. Scientists Worry over 'Bizarre' Trial for Failing to Predict Earthquake 2011-09-20T19:15:01.927Z For very long distances, eight places of decimals should be employed in logarithmic calculations; if seven places only are available very great care will be required to keep the last place true. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z Most office buildings windows are tinted and the logarithmic response of the human eye allows the tint to be very dark while still remining very easy to see through. Glass-Like Solar Cells Set Stage for Power-Producing Windows 2011-04-17T00:51:13Z We will also investigate logarithmic functions, which are closely related to exponential functions. Algebra and Trigonometry 2015-02-13T00:00:00Z The metal may drop as far as $1,670, which would be the ceiling of a long-term logarithmic chart, he said. Gold May Slide Before Extending Bull Rally: Technical Analysis 2011-09-12T04:58:04Z The quality of a galvanometer in this respect is best estimated by taking the logarithmic decrement of the oscillations when the movable system is set swinging. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 4 "G" to "Gaskell, Elizabeth" 2011-08-24T02:00:20.690Z For calculations of latitude and longitude, tables of the logarithmic values of ρ sin 1″, n sin 1″, and 2 n ρ sin 1″ are necessary. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z An integral possessing such logarithmic infinities is said to be of the third kind. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 "Frost" to "Fyzabad" 2011-08-15T02:00:28.473Z Three kinds of functions that are often useful in mathematical models are linear functions, exponential functions, and logarithmic functions. Algebra and Trigonometry 2015-02-13T00:00:00Z The company started with just six agents three years ago, and CEO Jay Rudman says "it's growing in just the logarithmic fashion we expected." The New Guard of Direct Selling 2011-07-11T04:00:00Z 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 These formulae give, in the case of k = 0.1a, values certain to eight logarithmic decimal places. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6 "Geodesy" to "Geometry" 2011-09-19T02:00:10.473Z The scale is meant to be logarithmic, meaning each level is considered 10 times as severe as the one below it. Japan Raises Danger Level at Power Plant 2011-03-19T00:25:27Z If the data is non-linear, we often consider an exponential or logarithmic model, though other models, such as quadratic models, may also be considered. Algebra and Trigonometry 2015-02-13T00:00:00Z The Richter scale records the power of earthquakes on a logarithmic scale, with each whole number increase corresponding to the release of about 31 times more energy. Green: Model Shows Intense Wave Power of Tsunami 2011-03-15T21:38:57Z And the new library at the end, with its greys and greens, its logarithmic computators at every table, was a miracle of mental-397- convenience. Marriage 2011-02-22T03:00:06.867Z Only in the exceptionally perfect vacuum referred to above did this logarithmic decrement sink to about one-twentieth of what it had commenced with. The Galaxy Vol. XXIII?March, 1877.?No. 3 2011-01-31T03:00:16.193Z The results give equations of the same logarithmic form as those obtained in a somewhat different manner in the theory of concentration cells described above, and have been verified by experiment. Encyclopaedia Britannica, 11th Edition, Volume 9, Slice 2 "Ehud" to "Electroscope" 2011-01-29T03:00:23.777Z In choosing between an exponential model and a logarithmic model, we look at the way the data curves. Algebra and Trigonometry 2015-02-13T00:00:00Z But when I pressed him on the science the only thing he said was that CO2 radiative forcing was logarithmic and complained that nobody knows this or talks about it. Scientists React to a Nobelist's Climate Thoughts 2010-09-17T22:30:00Z Decimal time and longitude would then correlate directly without the need for logarithmic conversion tables. 2010-01-15T08:50:00Z The scale is logarithmic, meaning that each number represents an order of magnitude jump in the amount of energy re-leased. 2010-01-13T17:51:00Z You see, my boy, it's rather an intricate table of logarithmic calculations that that scoundrel has pasted on this board. Astounding Stories of Super-Science, May, 1930 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 This critique is closely tied with Dyson’s comment about logarithmic response to CO2. Scientists React to a Nobelist's Climate Thoughts 2010-09-17T22:30:00Z Such treatment is apt to reduce a book on ballads and balladists to what Charles G. Leland terms 'mere logarithmic tables of variants.' The Balladists Famous Scots Series The correction for pressure has also been worked out in a series of tables and the logarithmic factor here corresponds to the ratio p/760, in which p is the observed barometer. Respiration Calorimeters for Studying the Respiratory Exchange and Energy Transformations of Man In this manner it calculates astronomical, logarithmic, and navigation tables, as well as tables of the powers and products of numbers. Pascal A logarithmic curve is always concave away from its vertical asymptote. Algebra and Trigonometry 2015-02-13T00:00:00Z The ingenious contrivances for representing logarithmic sines and tangents, so useful in navigation, on a scale. 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 first and third parts of the work contain logarithmic and other auxiliary tables, for the purpose of facilitating astronomical calculations. The Martyrs of Science, or, The lives of Galileo, Tycho Brahe, and Kepler If we amplify the Arctic breeze By logarithmic signs, And run through the isosceles Imaginary lines, We find that twice the half of one Is equal to the whole. The Book of Humorous Verse Temperature differences are logarithmic, you know, not arithmetic—the effective difference between his body temperature and ours is perhaps even greater than that between ours and that of melted iron. Spacehounds of IPC If we draw a line between any two of the points, most or all of the points between those two points lie above the line, so the graph is concave down, suggesting a logarithmic model. Algebra and Trigonometry 2015-02-13T00:00:00Z The tabulated logarithmic aid for correcting the apparent distance, and facilitating the reduction of the observations. 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. Slide rules are instruments for performing logarithmic calculations mechanically, and are extensively used, especially where Slide rules. only rough approximations are required. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" Caustic curves, spirals without number, succeeded, of which but one shall claim our notice,—the logarithmic spiral, first fully discussed by James Bernouilli. The Atlantic Monthly, Volume 03, No. 20, June, 1859 The incidence of computer viruses has been on a logarithmic increase for the past several years. Terminal Compromise: computer terrorism: when privacy and freedom are the victims: a novel Determine whether the data from the table could best be represented as a function that is linear, exponential, or logarithmic. Algebra and Trigonometry 2015-02-13T00:00:00Z Then I re-read the progressions, permutations, combinations; the binomial theorem, with indices and surds; the logarithmic theorem and series, converging and diverging. Men of Invention and Industry Near the balance a large logarithmic scale is fixed with a slide which has three indices only. Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary" Given the logarithmic curve y = e^x, the machine draws an identical curve. Scientific American Supplement, No. 288, July 9, 1881 That this quality of line is distinct from form may be shown by the simple experiment of turning a spiral—a logarithmic spiral, let us say—in different ways about its focus. The Psychology of Beauty Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic. Algebra and Trigonometry 2015-02-13T00:00:00Z Non-linearity: relations among dependent phenomena that cannot be described through a linear function, but through exponential and logarithmic functions, among others. The Civilization of Illiteracy By this characteristic we recognize the ‘logarithmic spiral.’ The Life of the Spider For the following exercises, solve for by converting the logarithmic equation to exponential form. Algebra and Trigonometry 2015-02-13T00:00:00Z For the following exercises, evaluate the natural logarithmic expression without using a calculator. Algebra and Trigonometry 2015-02-13T00:00:00Z For the following exercises, find the value of the number shown on each logarithmic scale. Algebra and Trigonometry 2015-02-13T00:00:00Z How do logarithmic graphs give us insight into situations? Algebra and Trigonometry 2015-02-13T00:00:00Z Picture a flexible thread wound round a logarithmic spiral. The Life of the Spider Because every logarithmic function is the inverse function of an exponential function, we can think of every output on a logarithmic graph as the input for the corresponding inverse exponential equation. Algebra and Trigonometry 2015-02-13T00:00:00Z We would need to create a corresponding new function by interchanging the input and the output; thus we would need to create a logarithmic model for this situation. Algebra and Trigonometry 2015-02-13T00:00:00Z All translations of the logarithmic function can be summarized by the general equation See Table 4. Algebra and Trigonometry 2015-02-13T00:00:00Z When finding the domain of a logarithmic function, therefore, it is important to remember that the domain consists only of positive real numbers. Algebra and Trigonometry 2015-02-13T00:00:00Z All, down to the common Snail-shell, are constructed according to logarithmic laws. The Life of the Spider That is, the argument of the logarithmic function must be greater than zero. Algebra and Trigonometry 2015-02-13T00:00:00Z Yes, if we know the function is a general logarithmic function. Algebra and Trigonometry 2015-02-13T00:00:00Z Knowledge of linear, exponential, logarithmic, and logistic graphs help us to develop models that best fit our data. Algebra and Trigonometry 2015-02-13T00:00:00Z Does the graph of a general logarithmic function have a horizontal asymptote? Algebra and Trigonometry 2015-02-13T00:00:00Z The Epeira’s construction, therefore, is a series of chords joining the intersections of a logarithmic spiral with a series of radii. The Life of the Spider Q&A Does every logarithmic equation have a solution? Algebra and Trigonometry 2015-02-13T00:00:00Z Then we use the fact that logarithmic functions are one-to-one to set the arguments equal to one another and solve for the unknown. Algebra and Trigonometry 2015-02-13T00:00:00Z Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic. Algebra and Trigonometry 2015-02-13T00:00:00Z We have used exponents to solve logarithmic equations and logarithms to solve exponential equations. Algebra and Trigonometry 2015-02-13T00:00:00Z The logarithmic spiral describes an endless number of circuits around its pole, to which it constantly draws nearer without ever being able to reach it. The Life of the Spider After plotting these data in a scatter plot, we notice that the shape of the data from the years 2000 to 2013 follow a logarithmic curve. Algebra and Trigonometry 2015-02-13T00:00:00Z In the case of positive data, which is the most common case, an exponential curve is always concave up, and a logarithmic curve always concave down. Algebra and Trigonometry 2015-02-13T00:00:00Z Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Algebra and Trigonometry 2015-02-13T00:00:00Z TRY IT #6 Does a linear, exponential, or logarithmic model best fit the data in Table 2? Algebra and Trigonometry 2015-02-13T00:00:00Z At least one of them, Planorbis vortex, for example, is a marvel of logarithmic whorls. The Life of the Spider Again, it is the way they increase or decrease that helps us determine whether a logarithmic model is best. Algebra and Trigonometry 2015-02-13T00:00:00Z Use logarithmic regression to fit a model to these data. Algebra and Trigonometry 2015-02-13T00:00:00Z How can the logarithmic equation be solved for using the properties of exponents? Algebra and Trigonometry 2015-02-13T00:00:00Z Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic. Algebra and Trigonometry 2015-02-13T00:00:00Z Now is this logarithmic spiral, with its curious properties, merely a conception of the geometers, combining number and extent, at will, so as to imagine a tenebrous abyss wherein to practise their analytical methods afterwards? The Life of the Spider Take a moment to recall some of the standard forms of equations we’ve worked with in the past: linear, quadratic, cubic, exponential, logarithmic, and so on. Algebra and Trigonometry 2015-02-13T00:00:00Z What might a scatterplot of data points look like if it were best described by a logarithmic model? Algebra and Trigonometry 2015-02-13T00:00:00Z For the following exercises, rewrite each equation in logarithmic form. Algebra and Trigonometry 2015-02-13T00:00:00Z To have done with this part of our subject, here is another property of the logarithmic spiral. The Life of the Spider Cut and polished length-wise, the fossil shows a magnificent logarithmic spiral, the general pattern of the dwelling which was a pearl palace, with numerous chambers traversed by a siphuncular corridor. The Life of the Spider Its extremity will not leave the plane and will describe a logarithmic spiral within it. The Life of the Spider The Epeira, therefore, is versed in the geometric secrets of the Ammonite and the Nautilus pompilus; she uses, in a simpler form, the logarithmic line dear to the Snail. The Life of the Spider |
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