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For example, you might hear a student say to her friend that her spelling test was "as easy as falling off a log."
VOA: special.2009.06.07
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We have a very, very strong discipline within the company, which is now 72 people, to log everything, to measure everything and to test everything.
我们公司内部,有很强的纪律性，现在公司已经有72人，负责记录一切，衡量一切，测试一切。
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All right? It's now something that I can search in constant time. And that's what's going to allow me to keep this thing as being log.
在固定的时间内搜索,这样就可以让时间复杂度保持在对数级,好的，考虑过了这些。
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Unlike blogs, Twitter users do not have to log onto the Web site to post updates.
VOA: special.2009.02.06
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And so, we can rewrite this as the work nRTln is equal to minus nRT log p1 over p2, nRTln or nRT log p2 over p1.
因此我们可以把这个式子改写一下,功等于负的，或者。
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The Whigs put up log cabins everywhere and offered free hard cider to everyone.
VOA: special.2009.01.22
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It'll say is this really what you ate, and if you ate it, then you say yes I ate this, and then it adds to the electronic log.
系统会问这是否确实是你吃的,如果确实是 就选择是,你的选择会被记入电子日志
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It is easier to fall off the log than to stay on it.
VOA: special.2009.06.07
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But mathematically, we've mentioned this before, log N or really to be precise, log base 2 of N, is the way you express this mathematically.
但从数学上说，之前我们已经提到过了，准确地说是log，N，以2为底N的对数，这就是它在数学上的表示。
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It said Harrison would be happier with a 2,000 dollar a year pension, a barrel of hard cider to drink, and a log cabin to live in.
VOA: special.2009.01.22
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A number of men, as one historian has written, I think quite effectively, "Mounted from log cabin to mansion" and I quote "On a stairway of cotton bales accumulating slaves as they went."
一些人就像一位历史学家写的那样,我觉得非常犀利,引述一段,"小木屋通往大厦的阶梯正是由,奴隶们用棉花包堆积成的"
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And their meaning is as easy to understand as "falling off a log."
VOA: special.2009.06.07
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For example, this is x=t, x=t^, you're going to have x=sin t and cos t and log t.
例如,这是x=t,x=t^,你还会遇到正弦,余弦,对数函数
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"Our health and wellness committee provided us with pedometers and there was a contest to see how many people could log ten thousand or more steps each day over a certain period.
VOA: special.2011.02.28
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If you go and work that out, log2 log of two and you have two log two, by math you can show that for the line r series m 2*log2 is equal to two natural log of two, which is 1 1.386 which is greater than one.
如果你把它计算出来，这二者的对数，你会得到2个，通过数学，你会得到第r列，第m个值,等于,也就是1。386，这大于。
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If you log on to Zazzle you can order a mug,t-shirt, even a tie promoting swine flu parties and their offer of a free H1N1 virus.
VOA: standard.2009.12.18
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Right? If that was the case in that code, then my complexity is no longer log, because I need linear access for each time I've got to go to the list, and it's going to Lisp be much worse than that.
这里的复杂度不再是对数的了，因为每次在列表中，查找需要线性访问,可能还要糟糕,其实，有些编程语言，如。
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And with this data, where students were able ; to implement last year their own E-trade-like website; whereby you have accounts and you log in your hand age of your users 10,000 virtual dollars and with them can they get stock quotes, by stocks, sell stocks and the like, all of this accomplished just after a few weeks time.
通过这些数据,学生们就可以做出类似电子商务的网站;,只要你有账号就能进入你的账户,里面有1万的虚拟美元,这样你就能去查询股票报价,进行买卖股票之类的事,这一切仅仅用了几个星期的时间就完成。
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So I have n operations log n times, n log n there we go, n log n. Took us a long time to get there, but it's a nice algorithm to have.
所以我log，n遍的n次操作，就得到了,虽然花了不少时间得到了这个结论。
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N 6 Sixteen, so that's 16 times log base 2 of 16 and though I'm writing small here, log base 2 of 16, 16 this gives me 4 'cause 2 to the 4 equals 16.
是多少呢？，Well，，N，is，what？,16，那就是16乘以以2为底16的对数6,在这儿我将2写小一些，以2为底16的对数是4，因为2^4等于。
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w This is just q plus w. There's w, RT1 ln q has to be R T1 log of V2 over V1.
而U等于q加，那是w，q应该是。
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k * n m plus k all times log n is in general going to be much better than k times n.
在普遍情况下要远远好于,实际情况要取决于n和k的取值。
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But that merging process only takes N steps, N*log N so that's N times log of N. Now, it's a little tricky to reason through this perhaps the first time, let's just take a very simple example and see if we can do a little sanity check here.
但这个合并过程只需要N步，所以时间复杂度是,第一次对此进行推论可能会有点儿棘手，我们举一个简单的例子,看看我们能否做一些完整性的检查。
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It would be nice if it was less than linear, but linear is nice because then I'm going to get that n log in kind of behavior.
那么就是一个不错的算法，但是线性方案也是很好的,因为我需要做n次的log级的行为。
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I could still do the linear case, which is order n or I could say, look, take the list, let's sort it and then search it. But in that case we said well to sort it was going to take n log n time, assuming I can do that.
我仍然可以做O的线性搜索,或者也可以以这个列表为例，我们先将其进行排序,然后再进行查找，但是在这种情况下,要花费n，log，n的时间去对其进行排序。
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Here's another way to think about why is this log.
那我来问一个完全不一样的问题。
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If I'm running at nanosecond speed, 1000 n, the size of the problem, whatever it is, is 1000, and I've got a log algorithm, it takes 10 nanoseconds to complete.
如果这个问题的规模，也就是n，是，如果这个问题是对数级的，这将会占据10纳秒的时间，你一眨眼的时间。
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log We're going to have the ratio of temperatures T1 and the ratio of these logs.
和这些,最后可以得到等于T2除以。
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Yeah. You're jumping slightly ahead of me, but basically, I'm done when this is equal to 1 right? Because I get down to the base case, so I'm done when b u is over 2 to the k is equal to 1, and you're absolutely right, that's when k is log base 2 of b.
因为这就是最基本的情况了，因此当b/2的k次方等于1的时候就停止了1,你说的太对了，就是k等于b的以2为底的对数的时候,你们都坐的挺靠后的啊，我不知道是不是我讲的不太明白？
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On the other hand, if I want to sort it first, OK, if I want to do sort and search, I want to sort it, it's going to take n log n time to sort it, and having done that, then I can search it in log n time.
我先排序，好的，如果我想排序再搜索，我要排序，这需要花n，log，n时间排序，然后做完了，我们能花log，n时间搜索,啊，哪一种更好呢？恩，呵呵。
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