On Sun, 30 Jul 2000 14:16:59 GMT, firstname.lastname@example.org (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(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!