Weber’s Law says that we perceive differences on a logarithmic, not a linear scale.

的名字来给它命名。韦伯定律，我们在对数尺度上感知物点，而是在线性尺度上。

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。

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的质疑。

In all seriousness, though, I'm pretty sure the index is meant to be logarithmic like earthquake magnitudes.

过讲真，我很确定这个指数本来是要像地震震级一样呈对数出现。

Each successive measurement increases logarithmically, meaning that each magnitude is 10 times more powerful than the one before it.

每一次连续的测量都呈对数增加，这意味着每一次测量的强度都是前一次测量的10倍。

Polynomials could also be used to approximate logarithmic and trigonometric functions, which are a real hassle to calculate by hand.

多项式也可以似对数和三角函数这些函数手算相当麻烦。

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，但我们要的这个对数却超级简单。

Because if you were to plot the progress, the progress looks like a log curve.

因为如果你要绘制进度，进度看起来就像一条对数曲线。

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

首先，研究人员使特定病毒蛋白的指令对数万亿个 mRNA 分子进行编码。

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

分贝使我们所说的对数尺度，数学家们应该知道这个。

Addition, subtraction, multiplication, division, squaring, cubing, roots, logarithms.

加法，减法，乘法，除法，平方，立方，根号，对数。

And so what he does is he plots that on a logarithmic scale.

是他将那数据绘制在对数尺度上。

And then you got two log rhythms.

然后你就得到了两个对数节奏。

So this is on a log scale.

所以这是对数尺度。

And more specifically, I want to talk about logarithmic relationship.

更具地说，我想讨论对数关系。

Now, interestingly, the logarithmic function has some similar properties to an exponential function.

有趣的是，对数函数与指数函数具有一些相似的性质。

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.

新公式依赖称为对数的数学概念。

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

仅是任何对数， 还有那些被称为“自然” 的对数。