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Topic: What is the proof for ln X = Int(1/x)?
Replies: 9   Last Post: Aug 2, 2000 10:31 AM

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John Savard

Posts: 601
Registered: 12/8/04
Re: What is the proof for ln X = Int(1/x)?
Posted: Aug 1, 2000 10:12 AM
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On Sun, 30 Jul 2000 14:16:59 GMT, ullrich@math.okstate.edu (David C.
Ullrich) wrote, in part:

> How you prove it depends on exactly how
>you defined Ln(x). For example sometimes Ln is
>defined to be the antiderivative of 1/x; with that
>definition the proof you ask about is sort of easy.
>With some other definition the proof will be
>different. So: what's the definition of Ln(x)
>that you have in mind?


Surely _that_ should be obvious. Since ln x is the logarithm of x to
the base e, that means to most people that ln x is defined as:

the function of x such that for x>0,

ln(1)=0

and

ln(a * (e^x)) = ln(a) + x.

or even more briefly that it is the inverse of e^x. Where e^x is
defined in terms of the value of e, and either by repeated
multiplication, or for x not an integer, in terms of limits of
repeatedly applying square roots!

John Savard (teneerf <-)
Now Available! The Secret of the Web's Most Overused Style of Frames!
http://home.ecn.ab.ca/~jsavard/frhome.htm







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