Which of the following is the correct order if they are ordered by asymptotic growth rates?
$F_1:n^{lg\,lgn}$
$F_2:(3/2)^n$
$F_3:(lg\,n)^{lg\, n}$
$F_4:n!$
$F_3$ can be re-written as $n^{lg\,lgn}$ using property $a^{log_bc}=c^{log_ba}$
So, $F_4 \gt F_2 \gt F_1=F_3$
Is my order correct?