## Solve $T(n) = 16T(n/2)+[n\log_2 {n}]^4$ using Master Theorem

The problem is to solve this using Master Theorem :

$$T(n) = 16T(n/2)+[n\log_2 {n}]^4$$

My attempt: I said that master theorem does not apply because the ratio of $$f/g = [\log_2 {n}]^4$$. This has no polynomial factor. But, when I looked at similar problems online, I saw some people apply case #2 here.

The version of the Master Theorem we use is as follows:

Our book also notes that in the first case not only must $$f$$ be smaller than $$n^{\log_b{a}}$$, it must polynomially smaller, that is, $$f$$ must be asymptotically smaller than $$n^{\log_b{a}}$$ by a factor of $$n^\varepsilon$$ for some constant $$\varepsilon>0$$. Similarly, in the third case, not only must $$f$$ be larger than $$n^{\log_b{a}}$$, it must polynomially larger.