If you have log n sorted lists , so now at leaf level (last level) u will hve log n lists each of size n/logn ,now when u will merge two lists at last level into 1 , u will get one list at second last level of size 2n/logn , Now likewise for 3rd last level u will get sorted list of size 4n/log n , so at each level u will get reduction in size of sorted list therefore work done at each level is of order(n) only since in total no of elements which are present are n and we are merging all n elements , and we have total no of levels as loglogn so total amount of work done is =no of levels *work done at each level =O(nloglogn)
becoz no of levels decrease logarithmically and we have log n sorted lists already present so it decreases by the number of sorted lists in logarthmic fashion and work done at each level means u r applying merge procedure for merging sorted lists so u are exploring all the n elements so total time complexity is O(nloglogn).