Which one is greater than other ,O(n*log^2n) or O(log^3n)??

Answer 1

You are comparing n logn logn to logn logn logn. It seems to me this comes down to n vs. logn - and that should not be hard to decide.

If this is homework then of course you need to fomally prove that O(n logn logn) is larger than O(logn logn logn). For that you need to show that there is a function f in the first class but not in the second. I would choose f to be the defining function n logn logn.

Answer 2

you mean O(n*log2(n)) vs O(log3(n))?
if it is so, O(n*log2(n)) complexity is greater

Answer 3

Thank you

Answer 4

I mean that the logarithm is raised to the power of 2 in the first term and to 3 in the second.