# Show that ln(e)=1.

1. Nov 8, 2009

### applegatecz

1. The problem statement, all variables and given/known data
Show that ln(e)=1.

2. Relevant equations
ln(x)=antiderivative from 1 to x of dt/t

3. 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.

2. Nov 8, 2009

### 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.

3. Nov 8, 2009

### applegatecz

Ah, I see! Thank you.