Recurrences that cannot be solved by the master theorem

You might wanna see the wikipedia link to the Master's theorem. They have a list of inadmissible equations, and the second one should suit your purposes.

To paraphrase the article for completeness, the following recurrence $$T(n) = 2T\left(\frac{n}{2}\right) + \frac{n}{\log(n)}$$ is inadmissible because the difference between $\frac{n}{\log(n)}$ and $n\log_b(a)$ is not polynomial.