Assume an integer x that x = 3*n and x = 4*m, so we got: n = m*4/3 ;
Compare the product : 3^n ~ 4^m; replace n, we got:
3^(4/3) ~ 4^m;
add log: m*4/3*log(3) ~ m * log(4) => 4/3log(3) ~ log(4). apparently, the left side is bigger than the right, so we choose factor 3.