This is why water can act as both an acid and a base.

对数运算的底数，或是说log下面的那个数字，把它作为指数运算的底数。

Secretary Sebelius faced hours of questions during that Congressional hearing yesterday.

部长西贝利厄斯在昨天的国会听证会上面对数小时的质疑。

They're what we use most in chemistry, and they're really easy to understand, and also what we base scientific notation on.

是的，没错，对数一眼看过去是有点吓人，但我们要用的这个对数却超级简单。

First, researchers encode trillions of mRNA molecules with the instructions for a specific viral protein.

首先，研究人员使用特定病毒蛋白的指令对数万亿个 mRNA 子进行编码。

Log base 2 of 8000 is roughly 13.

8000的以2为底的对数大约是13。

Decibels are in what we call a logarithmic scale, for the mathematicians out there.

贝使用我们所说的对数尺度，数家们应该知道这个。

So that said, oh yeah, let me take the logarithm of this formula.

那么说来，哦对了，让我来取这个公式的对数。

Very often, meetings also follow a similar logarithmic curve.

通常情况下，会议也遵循类似的对数曲线。

And the entropy is the log rhythm of that number.

熵是该数字的对数节奏。

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

新公式依赖于称为对数的数概念。

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。

Therefore pH which is the negative log of the hydronium is 7.

因此，水氢离子的负对数 pH 值为 7。

They don't stack linearly, they stack logarithmically and you can have an almost infinite outcome.

它们不是线性堆叠的，而是对数堆叠的，并且可以得到几乎无限的结果。

The consumer confidence index monitors consumer sentiment based on monthly interviews with thousands of households.

消费者信心指数根据每对数千户家庭的访谈来监测消费者的情绪。

Many of our learning processes also have a logarithmic shape to them.

许多习过程也呈现出对数曲线的特征。

Remember we take the negative log of that.

记住我们取它的负对数。

Log, there, is short for logarithm.

那里的“Log”是“logarithm”（对数）的缩写。

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, you know, adding two logarithms of the same base, how do you marry them into one term?

但是你知道，将两个同底数的对数相加，怎么把它们并成一个项呢？

And if we just look through them all, we can count up how many pairs have a given sum.

如果我们逐一查看它们，就可以统计出有多少对数的和等于给定的值。