A logarithm tells you what power a base number must be raised to in order to produce a given value.

对数说明一个底数的几次幂等于一个给定的值。

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OK, and for a given value of x, what we will do is we'll slice our graph by this plane parallel to the yz plane.

对于给定的x，我们要做的就是，用平行于yz平面的平面去切图像。

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For a given value of x, so that's a given slice, I have a range of values for y, that is, from this picture at the left most point on that slice to the rightmost point on that slice.

对于给定的x，对应一个切面，就可以得到一个y的取值范围，从图片上看，是从切面的最左边到最右边。

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By 2016,governments would be required to stabilize or begin reducing the percentage of their debt as measured against total gross domestic product, the value of all goods and services produced in a given country.

VOA: standard.2010.06.27

Again, same kind of reasoning says, given some value x, I happened to pick a small one here, what's an easy way to do this? Well, let's just start at one. That's my variable I'm going to change and check.

好，尤其是，让我们到这里来,让我给大家看看第二个例子,让我把这个注释掉，这是我要解决的，第二个问题，假设我想找到一些整数的,所有除数，我想要找出来这个数的所有的除数。

麻省理工公开课 - 计算机科学及编程导论课程节选

It's the old gray but dark philosophy that you should just look at value But, one of the things is when people have given up on a company--that's the perfect time.

就是那个陈旧黑暗的哲理,你应该只注重价值,但是，还有一种情况当人们都抛售了,某个公司的股票--那就是个极佳的时机。

耶鲁公开课 - 金融市场课程节选

Each area of improvement was given a point value and each potential solution was scored appropriately.

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Each letter is also given a point value based on difficulty, and some even award extra points by doubling or tripling the letter or overall word score.

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It is a value transfer system which is given value only by its users.

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