How do merge sort and quick sort differ? They both runs in O(n log n) complexity?

Question

While reading possible time complexity i found that time complexity O(log log n) exist for some algos,

Can any one explain an example which shows the calculation of the time complexity with O(log log n)

Answer 1

T(n)=3T(n/2)+n^2 give expression for runtimeTn if recursion can solve through mastertheorm otherwise indicated mastertheorm dosn't apply