Arrange the Following Functions in a List So Each Is $\log n ^ { 2 } , \log \log n , n \log n$

Short Answer

Arrange the following functions in a list so each is big-O of the next one in the list: $\log n ^ { 2 } , \log \log n , n \log n$ $\log \left( n ^ { 2 } + 1 \right) , \log 2 ^ { n }$