What is the order of the sum of log x? Let 
$$f(n)=\sum_{x=1}^n\log(x)$$
What is $O(f(n))$?
I know how to deal with sums of powers of $x$. But how to solve for a sum of logs?

Using Stirling's formula we have, for $n$ sufficiently large
$$
f(n)=\sum_{k=1}^n\log k=\log(n!)\simeq\log(\sqrt{2\pi}e^{-n}n^{n+1/2}).
$$
Hence
$$
O(f(n))=\log(\sqrt{2\pi}e^{-n}n^{n+1/2}).
$$
