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Formula
Calculate the value
$\log_{ 5 } {\left( 7 \right)} \times \log_{ 7 } {\left( 25 \right)}$
$2$
Calculate the value
$\log _{ 5 } { \left( 7 \right) } \log _{ \color{#FF6800}{ 7 } } { \left( \color{#FF6800}{ 25 } \right) }$
 Use $\log_{a}{x}=\dfrac{\log_{b}{x}}{\log_{b}{a}}$ to change a number of the logarithmic base 
$\log _{ 5 } { \left( 7 \right) } \times \color{#FF6800}{ \dfrac { \log _{ 5 } { \left( 25 \right) } } { \log _{ 5 } { \left( 7 \right) } } }$
$\log _{ \color{#FF6800}{ 5 } } { \left( \color{#FF6800}{ 7 } \right) } \times \dfrac { \log _{ 5 } { \left( 25 \right) } } { \log _{ \color{#FF6800}{ 5 } } { \left( \color{#FF6800}{ 7 } \right) } }$
 Reduce the expression with $\log _{ 5 } { \left( 7 \right) }$ , the greatest common devisor 
$\log _{ 5 } { \left( 25 \right) }$
$\log _{ 5 } { \left( \color{#FF6800}{ 25 } \right) }$
 Write the number in exponential form with base $5$
$\log _{ 5 } { \left( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \right) }$
$\log _{ \color{#FF6800}{ 5 } } { \left( \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } \right) }$
 Simplify the expression using $\log_{a}{a^{x}}=x\times\log_{a}{a}$
$\color{#FF6800}{ 2 } \log _{ \color{#FF6800}{ 5 } } { \left( \color{#FF6800}{ 5 } \right) }$
$2 \log _{ \color{#FF6800}{ 5 } } { \left( \color{#FF6800}{ 5 } \right) }$
 The logarithm is equal to 1 if a base is same as an antilogarithm 
$2 \times \color{#FF6800}{ 1 }$
$2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 }$
 Multiplying any number by 1 does not change the value 
$\color{#FF6800}{ 2 }$
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