Consider $n=2^{64}$.
$n^{logn}={2^{64*64}} =$ $2^{2^{12}}$ whereas ${(logn)}^n = 64^{2^{64}}=2^{6*{2^{64}}}\ge 2^{4*{2^{64}}}$$=2^{2^{68}}$.
Considering a greater $n = 2^{256}$,we have:
$n^{logn}=2^{256*256} $$=2^{2^{16}}$ whereas $(logn)^n = {2^{8*2^{258}}}$$=2^{2^{261}}$.
You can clearly see the difference in the growth rates of the two functions. Thus asymptotic growth of $n^{logn} \le (logn)^n $