Is log n! = Θ(n log n)?
$$\begin{align*}
\log n! &amp;=\sum_{i=1}^n\log i \\
                   &amp;\geq \sum_{i=\lceil n/2\rceil}^n \log i \\
                   &amp;\geq \sum_{i=\lceil n/2\rceil}^n \log \tfrac{n}{2} \\
                   &amp;\geq \tfrac{n}{2}\log \tfrac{n}{2} \\
                   &amp;= \tfrac{n}{2}\big(\log n - \log 2)\\
                   &amp;= \Omega(n\log n)\,.
\end{align*}$$