Arranging them in ascending order based on asymptotic growth rate:
$2^{log^{1/4}n}$
$2^{4{\sqrt{logn}}}$
$\frac{nlogn}{logn^{50}}$
$\frac{n^{1.65}}{2}$
$\frac{n^{2}}{(loglogn)^{56}}$
$\frac{n^{3}}{40}$
$\frac{n^{4}}{100}$
$n^{logn}$
$2^{{2}^{logn}}$
$(n!)^{3}$
If really needed then take log wisely while doing comparison between two functions, that means if anything common in both function then firstly cancel that and then apply log in order to avoid any error.
Also, if someone thinks this order has some errors somewhere, then kindly comment below so that I can correct it.
