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

部长西贝利厄斯在昨天国听证上对数小时质疑。

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

对数运算底数，或是说log那个数字，把它作为指数运算底数。

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

新公式依赖于称为对数数学概念。

And the entropy is the log rhythm of that number.

熵是该数字对数节奏。

Log base 2 of 8000 is roughly 13.

8000 以 2 为底对数大约是 13。

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

对于那里数学家来说，分贝是我们所说对数刻度。

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

不仅是任何对数， 有那些被称为“自然” 对数。

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月对数千家庭访谈来监测消费者情绪。

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指令对数万亿个 mRNA 分子进行编码。

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

横线是现在之前时间，纵线是聚落规模对数。

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

是，没错，对数一眼过去是有点吓人，但我们要用这个对数却超级简单。

And sometimes you see this with one more rearrangement still, where the information  is the negative log base 2 of the probability.

有时，您到这种情况， 需要进行一次重新排列，其中信息是以 2 为底概率负对数。

Strong bases meanwhile, like sodium hydroxide, consume large amounts of hydrogen ions leaving the concentration very low, so they 10d to have very high pHs.

那么pH，简单地表示为负该浓度以10为底对数，也就是7我这个小伙伴，成为了pH标度基础。

The neural network is trained on hundreds of millions of images paired with captions and can translate virtually any text prompt into a relevant image, even seemingly random prompts.

神经网络对数亿张配上字幕图像进行了训练，可以将几乎任何文本提示翻译成相关图像，甚至是似随机提示。

If Meg had wanted a reward for hours of patient labor, she received it in the hearty pressure of her father's hand and the approving smile he gave her.

如果梅格想要对数小时耐心劳动给予奖励，她在父亲用手用力按压和他给她赞许微笑中得到奖励。

And they can’t say it’s to save money, because at the very same time, they voted for trillions of dollars in new tax cuts, weighted towards those at the very top.

他们不说这是为了节约资金，因为此时此刻，他们对数以万亿税收优惠政策进行了投票，要为社最顶层人服务。

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.

要在知道声音强度情况求出声音响度，可以在每平方米 1 皮瓦参考强度上取其强度以 10 为底对数。

Fortunately, Dijkstra's algorithm was improved a few years later to take the number of nodes in the graph, times the log of the number of nodes, PLUS the number of lines.

幸运是，Dijkstra 算法在几年后得到改进，将图中节点数乘以节点数对数，再加上线数。

I've taken the log of the transform values so you can see them but if I don't, then it's clear most of the values, especially toward the edges are very small and these correspond to high frequencies.

我已经记录了变换值对数，以便您可以到它们，但如果我没有到它们，那么很明显大多数值（尤其是边缘值）都非常小，并且这些值对应于高频。

So, prior to the slide rule, we had to calculate logs using these long charts known as " log tables." So, the basis behind the slide rule were these very, very long books of incredibly accurate logarithmic tables.

因此，在计算尺出现之前，我们必须使用这些称为“对数表”长图表来计算对数。所以，计算尺背后基础是这些非常非常长书，里有极其精确对数表。