Extended Master Theorem:
If the recurrence is of the form $T(n)=aT(\frac{n}{b}) + \Theta (n^{k}log^{p}n) where, a\geq 1, b>1, k\geq 0$
and p is a real number.
1. if $a>b^{k}$, then T(n) = $\Theta(n^{log_{b}^{a}})$
2. if $a=b^{k}$
a. If p > -1 then $T(n)=\Theta(n^{log_{b}^{a}} log^{p+1}n)$
b. If p = -1 then $T(n)=\Theta(n^{log_{b}^{a}}loglogn)$
c. If p < -1, then $T(n)=\Theta(n^{log_{b}^{a}})$
3. If $a < b^{k}$
a. If $p\geq 0$, then $T(n)=\Theta(n^{k}log^{p}n)$
b. If p < 0, then $T(n) = O(n^{k}) $