How would you decide between $F_2$ and $F_3$?

4 votes

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?

$F_1:n^{lg\,lgn}$

$F_2:(3/2)^n$

$F_3:(lg\,n)^{lg\, n}$

$F_4:n!$

$F_3$ 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?

1

Ayush your order is spot on.

@srestha F4 comes first, followed by F2, not the other way around. Comment below in case you need explanation.

@srestha F4 comes first, followed by F2, not the other way around. Comment below in case you need explanation.

1

@goxul-Check this for better understanding

https://math.stackexchange.com/questions/111918/growth-of-exponential-functions-vs-polynomial