Master's theorem with f(n)=log n

Question

For master\'s theorem T(n) = a*T(n/b) + f(n) I am using 3 cases:

1. If a*f(n/b) = c*f(n) for some constant c > 1 then

Answer 1

When f(n)=log(n), the Master theorem is not applicable. You should use the more generalized theorem, Akra–Bazzi.

In result, T(n)=O(n).

source.

Another way to find a more specific proof of this result is looking for the proof of the computational complexity of the "Optimal Sorted Matrix Search" algorithm.