Is log^k(n) = (log n)^k ?

Question

Eg. log^2(n) = (log n)^2. Both are same.

So, can 2 be replaced with any number and still the equation remains same?

Answer 1

Yes. Notationally it's usually represented as log^k(n) rather than (log(n))^k, but they are equivalent. True for any base log and any value of the exponent.

It's similar to trig functions. We usually write sin²(x) rather than (sin(x))².