With the Big O notation, are there also possibilities for either the whole process to go to O(nlogn) or possibly subportions to the O(logn) range? There's also

With the Big O notation, are there also possibilities for either the whole process to go to O(nlogn) or possibly subportions to the O(logn) range? There's also a lot of math operations over the years that have gone to O(Nª) where 1 < a < 2.