What is the time complexity of an $O((\ln n)^{\ln n})$ algorithm?

Question

How can the time complexity of an $O((\ln n)^{\ln n})$ algorithm be simplified and compared to some other time complexities?

Answer 1

some very simple calculation: $\log n^{\log n} = v = e^{\log v} = n^{\log \log n}$ give some options depending on what you need.