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Formula
Calculate the value
$\log_{ 2 } {\left( \log_{2} {\left( 3 \right)} \right)} + \log_{2} {\left( \log_{ 3 } {\left( 4 \right)} \right)}$
$1$
Calculate the value
$\log _{ \color{#FF6800}{ 2 } } { \left( \log _{ \color{#FF6800}{ 2 } } { \left( \color{#FF6800}{ 3 } \right) } \right) } + \log _{ \color{#FF6800}{ 2 } } { \left( \log _{ \color{#FF6800}{ 3 } } { \left( \color{#FF6800}{ 4 } \right) } \right) }$
 Calculate addition of logarithm 
$\log _{ \color{#FF6800}{ 2 } } { \left( \log _{ \color{#FF6800}{ 2 } } { \left( \color{#FF6800}{ 4 } \right) } \right) }$
$\log _{ 2 } { \left( \log _{ 2 } { \left( \color{#FF6800}{ 4 } \right) } \right) }$
 Write the number in exponential form with base $2$
$\log _{ 2 } { \left( \log _{ 2 } { \left( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \right) } \right) }$
$\log _{ 2 } { \left( \log _{ \color{#FF6800}{ 2 } } { \left( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \right) } \right) }$
 Simplify the expression using $\log_{a}{a^{x}}=x\times\log_{a}{a}$
$\log _{ 2 } { \left( \color{#FF6800}{ 2 } \log _{ \color{#FF6800}{ 2 } } { \left( \color{#FF6800}{ 2 } \right) } \right) }$
$\log _{ 2 } { \left( 2 \log _{ \color{#FF6800}{ 2 } } { \left( \color{#FF6800}{ 2 } \right) } \right) }$
 The logarithm is equal to 1 if a base is same as an antilogarithm 
$\log _{ 2 } { \left( 2 \times \color{#FF6800}{ 1 } \right) }$
$\log _{ 2 } { \left( 2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \right) }$
 Multiplying any number by 1 does not change the value 
$\log _{ 2 } { \left( \color{#FF6800}{ 2 } \right) }$
$\log _{ \color{#FF6800}{ 2 } } { \left( \color{#FF6800}{ 2 } \right) }$
 The logarithm is equal to 1 if a base is same as an antilogarithm 
$\color{#FF6800}{ 1 }$
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