Mathematics - Sequence & Series Question with Solution | TestHub

Let$m$be the minimum possible value of${\log }_3\left(3^{y_1}+3^{y_2}+3^{y_3}\right)$, where$y_1, y_2, y_3$are real numbers for which$y_1+y_2+y_3=9$. Let$M$be the maximum possible value of$\left({\log }_3{x}_1+{\text{log}}_3 x_2+{\text{log}}_3 x_3\right)$, where$x_1, x_2, x_3$are positive real numbers for which$x_1+x_2+x_3=9$. Then the value of${\text{log}}_2 \left(m^3\right)+{\text{log}}_3\left(M^2\right)$is