Solving $T(n)= 3T(n/4)+ n\log n$ without the master method

Question

How can one solve $$T(n)= 3T\left(\frac{n}{4}\right) + n\cdot \log n$$ without using the master method?

I know it has a solution using the master theorem from this link.

Answer 1

Hint:

The master theorem is the result of observing the tree associated to the recursive relation $T(n)$. So, one possible way can be considering draw by yourself this tree, begin with the root, in this case, $n\log n$ and descending with three nodes, each one $T(n/4)$, and so on. When you see the pattern, look at each level of the tree, then sum up all nodes, and sum all levels, the total should give you an answer.