I want to show that
$$\log^{i} n \in O(n^{j})$$
I tried to apply L'Hospital and came up with the following:
$$\lim\limits_{n \rightarrow \infty}{\frac{\log^{i} n}{n^{j}}} =$$ $$\lim\limits_{n \rightarrow \infty}{\frac{\log^{i-1} (1/n) n}{j*n^{j-1}}} =$$ $$\lim\limits_{n \rightarrow \infty}{\frac{\log^{i-1} n}{n^{j}}}$$
Now I am kind of stuck since I don't no how to make a statement out of this. Help would be greatly appreciated!