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$\color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ a } } = \color{#FF6800}{ 243 } ^ { \color{#FF6800}{ 3 } }$

$ $ Solve an exponential equation (inequality) by taking the logarithm on both sides $ $

$\log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 2 } } \right) } \color{#FF6800}{ + } \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ a } } \right) } = \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 243 } ^ { \color{#FF6800}{ 3 } } \right) }$

$\log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 2 } } \right) } \color{#FF6800}{ + } \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ a } } \right) } = \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 243 } ^ { \color{#FF6800}{ 3 } } \right) }$

$ $ Solve the equation $ $

$\color{#FF6800}{ a } = \color{#FF6800}{ 11 }$