Is log(n) in complexity class P?
Wikipedia says:


  An algorithm is said to be of polynomial time if its running time is upper bounded by a polynomial expression in the size of the input for the algorithm.


$\mathcal{O}(\log n)$ is upper bounded by $\mathcal{O}(n)$, and $\mathcal{O}(n \log n )$ is upper bounded by $\mathcal{O}(n^2)$, therefore they are both in $P$.