Show that there does not exist a strictly increasing function $f:\mathbb{N}\rightarrow\mathbb{N}$ satisfying
$f(2)=3$ $f(mn)=f(m)f(n)\forall m,n\in\mathbb{N}$
Progress: Assume the function exists. Let $f(3)=k$ Since $2^3 < 3^2$, $3^2=f(2)^3=f(2^3)
I've messed around with knowing $f(3)=6$ and $f(2)=3$ but I am stuck.