Big Oh Analysis simplification

Question

I am trying to get a better understanding of big oh algorithm analysis.
Is there a way to simplify

5n⋅(log(n))³.

I am thinking it simplifies to:

n⋅(log(n))³

Answer 1

That's correct. The basic idea here is to remove constant terms where they have no effect of the rate of growth.

In this case, you have:

(5) x (n) x (log(n)^3)

and, since the 5 would simply change 1,2,3,4,5 into 5,10,15,20,25, it has no effect on the growth rate.

So it can be removed.