But let me go back to these sines, cosines and logarithms.

但让我们再来说说正弦、余弦和对数函数。

That negative 5, is your base 10 logarithm.

这到底为什么会发生呢？

And a little bit about pOH, which can be calculated with logarithms, also with subtraction.

它们通常也有很低的pH值。

You learned about logarithms and how you can use them to calculate the pH of a substance.

因为它们使氢离子浓度大幅提升。

The new formula relies on the mathematical concept known as logarithms.

新公式依赖于称为对数的数学概念。

And not just any logarithms, but those known as " natural" ones.

不仅是任何对数， 还有那些被称为“自然” 的对数。

So, yeah, logarithms can seem a little bit scary at first, but the ones that we're using here are super easy.

我们通常把水看做一种完美的中性物质。

Though he had an interest in logarithm and logistics, he wanted to be a logician.

虽然他对对数和后勤学感兴地，他想成为一名逻辑学家。

The horizontal line is time before present, and the vertical line as the logarithm of sizes of settlements.

横线是现在之前的时间，纵线是聚落规模的对数。

But one thing you need to remember about the pH scale, because pH is calculated from a negative logarithm, it turns everything backward.

而且由于它是一个十分特殊的反应，因此它有一个独特的名字——水的电离常数，也就是Kw。

To figure out a dog's biological age, they say, multiply the natural logarithm of the dog's age in years by 16. Then add 31.

他们说，要计算狗的生理年龄， 请将狗的年龄（以年为单位）的自然对数乘以 16， 然后再加上 31。

So, for example, I don't think that being a math person means that you can recite the formulas between the sines, cosines, tangents and to use logarithms and exponentials interchangeably.

所以，比如，我认为成为数学家不是指你要能背诵正弦、余弦、正切的函数公式和转化运用对数和指数。

To find the loudness of a sound when you know its intensity, you take the base-10 logarithm of its intensity, over the reference intensity of 1 picowatt per square meter.

要在知道声音强度的情况下求出声音的响度，可以在每平方米 1 皮瓦的参考强度上取其强度的以 10 为底的对数。