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Formula
Calculate the value
$\log_{ 3 } {\left( \dfrac{ 1 }{ 81 } \right)}$
$- 4$
Calculate the value
$\log _{ 3 } { \left( \dfrac { \color{#FF6800}{ 1 } } { 81 } \right) }$
 Since the logarithm of antilogarithm numbers and numerator is 1 as the fraction, add minus to the logarithm and take reciprocal to antilogarithm numbers 
$\color{#FF6800}{ - } \log _{ 3 } { \left( \color{#FF6800}{ 81 } \right) }$
$- \log _{ 3 } { \left( \color{#FF6800}{ 81 } \right) }$
 Write the number in exponential form with base $3$
$- \log _{ 3 } { \left( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \right) }$
$- \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 4 } } \right) }$
 Simplify the expression using $\log_{a}{a^{x}}=x\times\log_{a}{a}$
$- \left ( \color{#FF6800}{ 4 } \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } \right) } \right )$
$- \left ( 4 \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 3 } \right) } \right )$
 The logarithm is equal to 1 if a base is same as an antilogarithm 
$- \left ( 4 \times \color{#FF6800}{ 1 } \right )$
$- \left ( 4 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \right )$
 Multiplying any number by 1 does not change the value 
$- \color{#FF6800}{ 4 }$
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