1. log²n =(log n)2 : Here square is on logn not on n.
2. logn² : Here square is on n.So first calculate n2 than take the log.
So log²n =(log n)2 ≠ logn2
Consider n=100
Assuming base to be 10
log²n = (log n)2 = (log 100)2 = (2)2 =4
logn² = log1002 = log10000 = 4
loglogn =loglog100 =log(log100)=log2
(log n)2 = (log 100)2 = (2)2 =4