$\displaystyle 3.2^n<n!$ for any positive interger n greater than 4

i did the base step

$\displaystyle 3\times2^5<5!$

$\displaystyle 96<120$

now the n+1 step, i can do some of but get stuck

$\displaystyle 3\times2^{n+1}<(n+1)!$

$\displaystyle 3\times2^n\times2<n!\times(n+1)$

what do i do from here? thanks.