Binary search algorithm - worst-case complexity
That's a way to do it. Sometimes it's easier to go the other way round: What is the size of the largest array where binary search will locate an item or determine it's not there, using k comparisons? And it turns out that the largest array has size $2^k - 1$. And then you reverse this. 

Understanding the master method is very useful if you have to pass a test that tests whether you understand the master method. But be prepared to have more practical problem where the only method that works is the "turn on your brain" method. A simple example is the Greatest Common Divisor algorithm.