Comparing $\;2^n\;$ and $\;n!\;$
I need to rewrite one or the other so they can be more easily compared (i.e. have similar form). Because of the factorial, I'm a little lost as to how to compare the two functions. Normally, I would take the logarithm when trying to re-express a power like $2^n$, but I don't think this will work, since I don't know how to take the logarithm of a factorial, if at all.
Might the series expansions of either functions be the right approach? If not could, someone point me in the right direction?