
Re: What is the proof for ln X = Int(1/x)?
Posted:
Aug 1, 2000 10:12 AM


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

