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