Let $k\geq 1, c>1$. I want to prove that $n^k = {\cal O }(c^n)$, that is, $\exists n_0, b>0 \ s.t. \ \forall n\geq n_0, \ n^k\leq b c^n$
I'm struggling to prove this result, now I'm just trying to use induction to prove $\log_c (n^k/b) \leq n$, for some constants $n_0,b>0$, but this is not going well. Basically if I could prove this statement the rest will be very easy. Any sugsestions?