Let m be the minimum possible value of `log_(3)(3^(y_(1))+3^(y_(2))+3^(y_(3)))`. Where `y_(1),y_(2),y_(3)` are real number for which `y_(1)+y_(2)+y_(3)=9` Let M be the maxmum possible value of `(log3x_(1)+log_(3) x_(2)+ log_(3) x_(2))` where `x_(1), x_(2), x_(3)` are positive real numbers for whcih `x_(1)+x_(2)+x_(3)=9` then the value of `log_(2)m^(3)+log_(3)(M^(2))` is _____

Answer

8