# recurrence function $T(n) = 27T(\frac{n}{3}) + 27^4\log(n)$

Considering the recurrence function:

$$\mathrm{T}(n) = 27\cdot\mathrm{T}(\frac{n}{3}) + 27^4\cdot\log(n)$$

Can this question be solved using the Master Theorem? If yes, how?

Recall that the master theorem allows you to solve recurrences such as $$T(n) = aT(n/b)+f(n)$$ if there is an $$\epsilon$$ s.t. $$f(n) = \Theta(n^{log_b(a)+\epsilon})$$ and $$c$$ such that $$af(n/b) \leq cf(n)$$. In your case, $$f(n)$$ is $$27^4log(n)$$. Because there is no $$k$$ such that $$log(n)$$ is $$\Theta(n^k)$$ the answer is no, you cannot solve the recurrence with the master theorem.