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$\color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ + } \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } = \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ b } }$

$ $ Invert the left and right terms to solve the exponential equation (inequality) $ $

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

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

$ $ Add the forms of the powers with the same bases and exponents $ $

$b = \log _{ 3 } { \left( \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \right) }$

$b = \log _{ 3 } { \left( \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 9 } ^ { \color{#FF6800}{ 3 } } \right) }$

$ $ Simplify the expression $ $

$b = \log _{ 3 } { \left( \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 729 } \right) }$

$b = \log _{ 3 } { \left( \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ 729 } \right) }$

$ $ Multiply $ 3 $ and $ 729$

$b = \log _{ 3 } { \left( \color{#FF6800}{ 2187 } \right) }$

$b = \log _{ 3 } { \left( \color{#FF6800}{ 2187 } \right) }$

$ $ Write the number in exponential form with base $ 3$

$b = \log _{ 3 } { \left( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 7 } } \right) }$

$b = \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 7 } } \right) }$

$ $ Simplify the expression using $ \log_{a}{a^{x}}=x\times\log_{a}{a}$

$b = \color{#FF6800}{ 7 } \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } \right) }$

$b = 7 \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } \right) }$

$ $ The logarithm is equal to 1 if a base is same as an antilogarithm $ $

$b = 7 \times \color{#FF6800}{ 1 }$

$b = 7 \color{#FF6800}{ \times } \color{#FF6800}{ 1 }$

$ $ Multiplying any number by 1 does not change the value $ $

$b = \color{#FF6800}{ 7 }$