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Solve the equation
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$y = \log _{ x } { \left( 4 \right) }$
$y = \dfrac { 2 } { 3 }$
$x = 8$
Solve the equation
$\log _{ \color{#FF6800}{ x } } { \left( \color{#FF6800}{ 4 } \right) } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 3 } } }$
$ $ Find the interval that satisfies the basic condition of each formula $ $
$\log _{ \color{#FF6800}{ x } } { \left( \color{#FF6800}{ 4 } \right) } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 3 } } } \left ( \text{However (or only)} \color{#FF6800}{ x } > \color{#FF6800}{ 0 } , \color{#FF6800}{ x } \neq \color{#FF6800}{ 1 } \right )$
$\log _{ \color{#FF6800}{ x } } { \left( \color{#FF6800}{ 4 } \right) } = \color{#FF6800}{ \dfrac { \color{#FF6800}{ 2 } } { \color{#FF6800}{ 3 } } } \left ( \text{However (or only)} x > 0 , x \neq 1 \right )$
$ $ Organize the equation using the logarithm definition $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 8 } \left ( \text{However (or only)} x > 0 , x \neq 1 \right )$
$\color{#FF6800}{ x } = \color{#FF6800}{ 8 } \left ( \text{However (or only)} \color{#FF6800}{ x } > \color{#FF6800}{ 0 } , \color{#FF6800}{ x } \neq \color{#FF6800}{ 1 } \right )$
$ $ Confirm if the solution exists in the domain $ $
$\color{#FF6800}{ x } = \color{#FF6800}{ 8 }$
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