I am trying to solve this issue but I do not know how to handle the division by $O(\sqrt{n})$.
Prove the following using limits and L’Hôpital’s Rule: That $\log n$ is $O(\sqrt{n})$.
$ \begin{align*} \lim_{n \rightarrow \infty}\frac{\log n}{\sqrt{n}} &= \lim_{n \rightarrow \infty}\frac{\log n}{10^{1/2 \log n}}\\ \end{align*} $