I am given that $T(n) = 6T(n/4) + n \lg n$ and want to find $\Theta(T(n))$. Below is what I have typed up for my solution so far; I asked my professor because I was unsure as to how I could assure that the result is not just Big Oh, but also Big Theta and he informed me that I could have applied the Master Theorem to this recurrence relation. I however do not see how it applies. Below is images of the pdf of my current solution.
Could someone either verify that my solution is valid and point me in a direction of how I can assure that my solution is a tight bound or explain the application of the master theorem in this case to me?
