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So looking at large values of N and M, this formula is basically  $lg_{m}(Nm) = h$ because $Nm$ is the dominating term. So if $m^'=m^2$, $n=m^2$,  then the height of $m^' $n  is double M$. $lg(Nm) = h$  $lg(N(m^')^2 $lg(N(n)^2  = h$ $2lg(N) = h$