Proving the Natural Logarithm Property: ln(e)=1

[applegatecz]

Homework Statement

Show that ln(e)=1.

Homework Equations

ln(x)=antiderivative from 1 to x of dt/t

The Attempt at a Solution

I assume we have to use the fact that e= lim as n->infinity of (1+1/n)^n, and perhaps can apply l'Hopital's rule to transform that limit -- but I'm not sure where to go from there.

 

[jgens]

If e = \lim_{n \to \infty}(1 + \frac{1}{n})^n, then we know that ln(e) = \lim_{n \to \infty}(n)ln(1 + \frac{1}{n}). Now put this in a form where you can apply L'Hospital's Rule.

 

[applegatecz]

Ah, I see! Thank you.