What is the meaning of $n\log^2(n)$

Question

I know this seems ridiculously an obvious thing but: What does $n\log^2(n)$ mean? Does it mean $n\log (\log(n))$ or $n\log(n)^2$? I am trying to compare it with $n\log(n)$ to check which one of the two is bigger for large $n\in \mathbb{N}$.

Answer 1

I would say that it means $$n[\log(n)]^2.$$

Answer 2

The usual interpretation is $n\log^2n=n(\log n)^2$.

Answer 3

It's simple exponentiation:

$$\log^2(n) = \log(n)*\log(n)$$

Answer 4

Maybe you have seen the notation $\cos^2(x)$, as in $\cos^2(x)+\sin^2(x) = 1$. This is just notation, and it means $\cos^2(x) = (\cos(x))^2$.

Similarly for $\log$.