How would you compare $O((\log n)^k)$ in relation to $O(n^c)$, $n,c \in \mathbb{N}\*$ ? I'm very stuck on how to go about this.

I specifically need to see how $O((\log n)^{2021})$ relates to $O(n^3)$ and $O(\log n \cdot n^2)$. Thanks for any help I'm really stumped on this one. I tried using l'hôpital or proof by induction but I'm heading nowhere.