lim (1+1/x)^x as x->infinity

Good afternoon,

I am working on a problem that asks to find the following limit:

$\displaystyle

lim_{x\rightarrow\infty}(1+\frac{1}{x})^x

$

This should be equal to *e*, but I am having some difficulty remembering why.

I checked WolframAlpha and was provided with the following:

$\displaystyle

lim_{x\rightarrow\infty}(1+\frac{1}{x})^x

$

Indeterminate form of type $\displaystyle 1^\infty$. Transform using

$\displaystyle

lim_{x\rightarrow\infty}(1+\frac{1}{x})^x

$ = $\displaystyle

lim_{e^{x\rightarrow\infty}}x log(1+\frac{1}{x})

$

Where did this come from?