Help on a Simple Limit ?

[Randy Yates]

I'm trying to find

\lim_{x\rightarrow 0} \frac{2^x - 1}{x}

I know the answer (ln(2)). This is not homework. I'm simply wanting to
determine the way to solve such a limit.

I've applied L'Hopital without success. I've alse tried taking the limit
of \exp{\frac{2^x - 1}{x}}, without success.

I'd appreciate if someone could give me a hint without divulging the
entire solution to give me a chance to solve it on my own first.

[Randy Yates]

Never mind! I got it! I kept on making the mistake (after applying
L'Hopital) that d(2^x) / dx = x*2^{x-1}, which of course is WRONG!

Thanks for, well, allowing me to ask the question!