Prove that $3^n>n^4$ if $n\geq8$ Proving that $3^n>n^4$ if $n\geq8$
I tried mathematical induction start from $n=8$ as the base case, but I'm stuck when I have to use the fact that the statement is true for $n=k$ to prove $n=k+1$.  Any ideas?
Thanks!

First show the base case. Then assume $3^k>k^4$. Hence, $3^{k+1}=3*3^k>3k^4>(k+1)^4$
