Prove or disprove $O(n)^{O(\log_2 n)} = O(2^n)$
My naive proof as follows :
There exist a positive $c$ and $n_0$ such that
$$0\leq f(n) \leq cn^{\log_2 n} = c\cdot 2^{(\log_2 n)^2} \leq c\cdot 2^n\space \space \forall n\geq n_0$$
And now, I don't know how to finish the proof properly.
Thank you all sincerely.