Firstly, note that $4^n\cdot (5^n)^2=10^{2n}$, so if we let $4^n=a_n\cdot 10^{\alpha_n}$ and $5^n=b_n\cdot 10^{\beta_n}$, with $1\leq a_n,b_n<10$, we must have $a_nb_n^2=10^t$ where $0\leq t<3$. Using the fact that $s=\lfloor 10a_n\rfloor=\lfloor 10b_n\rfloor$, we must have $10^3\leq s^3\leq 10^{t+3}<(s+1)^3\leq 100^3=10^6$. Therefore $s=\lfloor \sqrt[3]{10^{t+3}}\rfloor$, where $0\leq t<3$. If $t=0$, we would have to have the equalities $10=s=10a_n=10b_n$, which imply that $4^n$ and $5^n$ are powers of $10$, which isn't possible since $n>0$. We therefore conclude that the only possible values for $s$ are $s=\lfloor \sqrt[3]{10^{4}}\rfloor=21$ and $s=\lfloor \sqrt[3]{10^{5}}\rfloor=46$.