What is the difference between $\log^2(n)$, $\log(n)^2$, $(\log n)^2$, $\log (n^2)$ and $\log \log n$?
For the first one, you can find an answer here:


  (log(n))² means log²(n)


And from this question for example you can guess that:


  log(n)² = (log(n))²


So both the first and the second essentially mean 


  (log(n)) × (log(n))


(Unfortunately, not with more reliable sources than stackexchange...)