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$\log_{ 3 } {\left( \sqrt{ 81 } \right)} - \sqrt[3]{ 27 }$
$- 1$
Calculate the value
$\log _{ 3 } { \left( \sqrt{ \color{#FF6800}{ 81 } } \right) } - \sqrt[ 3 ]{ 27 }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$\log _{ 3 } { \left( \color{#FF6800}{ 9 } \right) } - \sqrt[ 3 ]{ 27 }$
$\log _{ 3 } { \left( \color{#FF6800}{ 9 } \right) } - \sqrt[ 3 ]{ 27 }$
$ $ Write the number in exponential form with base $ 3$
$\log _{ 3 } { \left( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \right) } - \sqrt[ 3 ]{ 27 }$
$\log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } \right) } - \sqrt[ 3 ]{ 27 }$
$ $ Simplify the expression using $ \log_{a}{a^{x}}=x\times\log_{a}{a}$
$\color{#FF6800}{ 2 } \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } \right) } - \sqrt[ 3 ]{ 27 }$
$2 \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } \right) } - \sqrt[ 3 ]{ 27 }$
$ $ The logarithm is equal to 1 if a base is same as an antilogarithm $ $
$2 \times \color{#FF6800}{ 1 } - \sqrt[ 3 ]{ 27 }$
$2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } - \sqrt[ 3 ]{ 27 }$
$ $ Multiplying any number by 1 does not change the value $ $
$\color{#FF6800}{ 2 } - \sqrt[ 3 ]{ 27 }$
$2 - \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ 27 } }$
$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $
$2 - \color{#FF6800}{ 3 }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ - } \color{#FF6800}{ 3 }$
$ $ Subtract $ 3 $ from $ 2$
$\color{#FF6800}{ - } \color{#FF6800}{ 1 }$
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