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 ( $\log _ { 3 } x _ { 1 } + \log _ { 3 } x _ { 2 } + \log _ { 3 } x _ { 3 }$ ), where $x _ { 1 } , x _ { 2 } , x _ { 3 }$ are positive real numbers for which $x _ { 1 } + x _ { 2 } + x _ { 3 } = 9$. Then the value of $\log _ { 2 } \left( m ^ { 3 } \right) + \log _ { 3 } \left( M ^ { 2 } \right)$ is
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 ( $\log _ { 3 } x _ { 1 } + \log _ { 3 } x _ { 2 } + \log _ { 3 } x _ { 3 }$ ), where $x _ { 1 } , x _ { 2 } , x _ { 3 }$ are positive real numbers for which $x _ { 1 } + x _ { 2 } + x _ { 3 } = 9$. Then the value of $\log _ { 2 } \left( m ^ { 3 } \right) + \log _ { 3 } \left( M ^ { 2 } \right)$ is