Are polynomials *always* asymptotically larger than polylogarithms?

Question

Is it always the case that asymptotically, for any $c,d>0$ it holds that $n^c$ is asymptotically larger than log$^d(n)$?

That is, if $f=O(n^c)$ and $g=\Omega(log^d(n))$, is $f/g$ unbounded as $n\rightarrow\infty?$