how to solve the following recurrence $T(n) \leq 2c (\lfloor \frac{n}{2} \rfloor + 17) \log (\lfloor \frac{n}{2} \rfloor + 17) + n$.

Question

The title is pretty much self-explanatory. I don't think I have the necessary math skills to solve the recurrence. Thanks in advance.

Edit:

My question is how to simplify $ ... \log (\lfloor \frac{n}{2} \rfloor + 17) ...$.

Nowhere in the basic log properties do I see how to expand the following: log(x + y). Thus I am not sure hot to proceed.