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.

他们不会说这是为节约资金，因为此时此刻，他们对数以万亿税收优惠政策投票，要为社会最顶层人服务。

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训练，可以将几乎任何文本提示翻译成相关图像，甚至是看似随机提示。

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pH标度基础。

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，对数一眼看过去是有点吓人，但我们要用这个对数却超级简单。

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

对数运算底数，或是说log下面那个数字，把它作为指数运算底数。

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

分贝使用我们所说对数尺度，数学家们应该知道这个。

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

那么说来，哦对，让我来取这个公式对数。

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

许多学习过程也呈现出对数曲线。

Remember we take the negative log of that.

记住我们取它负对数。

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

它们不是线性堆叠，而是对数堆叠，并且可以得到几乎无限结果。

And it falls into a very simple relationship between the temperature and the logarithm of time, which for many of us, it makes life, you know, even though a little bit more complicated, it still remains quite easy and tangible.

这形成一个非常简单温度与时间对数之间关系，对于我们许多人来说，尽管这使得生活稍微复杂一些，但它仍然保持相当简单和直观。

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，里面有极其精确对数表。

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.

我已经记录变换值对数，以便您可以看到它们，但如果我没有看到它们，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。

The abundance ratio serves as a crucial indicator of a star's chemical composition, typically expressed as the logarithm of the ratio between two metallic elements in the star relative to their abundance in the Sun.

丰度比作为恒星化学组成一个关键指标，通常表示为恒星中两种金属元素丰度比相对于太阳中这两种元素丰度比对数。

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，几年后Dijkstra算法得到改，其效率取决于图中节点数量乘以节点数量对数，再加上边数量。

In air, this reduction would make a sound seem one-quarter as loud (since the decibel scale is logarithmic, every ten decibels lost roughly equates to a reduction by half in volume).

在空气中，这种减弱会使声音听起来只有原来四分之一（因为分贝尺度是对数，每损失十分贝大约相当于音量减少一半）。

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，她会在父亲用手用力按压和他给她赞许微笑中得到奖励。

Formerly, it stated that the logarithm of the period of a Cepheid variable is linearly, i.e. directly related to the star's average measured brightness.

以前，它表明造父变星周期对数与其平均观测亮度呈线性关系，即直接相关。

One idea might be that it should be the number of pairs  of chords since every intersection point comes from two different chords.

一个想法可能是它应该是弦对数，因为每个交点都来自两条不同弦。

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户家庭访谈来监测消费者情绪。