Solve recurrence relation using master theorem

Question

Maybe anyone has idea how to solve this recurrence relation using master theorem? $$T(n)=2T(\frac{n}{2})+log_2n+10$$ So $$a=2, b=2,f(n)=log_2n+10$$ I think that I should use first case, because $$\log_2n+10<n^{log_22}$$ So I should proof that $$\lim_{n\to\infty}\frac{log_2n+10}{n^{1-\epsilon}}=0$$ But no idea how to proof that.

Answer 1

Hint: Take $\epsilon= \frac{1}{2}$. Then $\lim_{n\to\infty}\frac{log_2n+10}{n^{1-\epsilon}}=\lim_{n\to\infty}\frac{log_2n}{\sqrt{n}}$ and use L'Hospital rule.