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Formula
Calculate the value
Find the value of the common log
$\log {\left( 200 \right)}$
$2 + \log _{ 10 } { \left( 2 \right) }$
Calculate the value
$\log _{ 10 } { \left( \color{#FF6800}{ 200 } \right) }$
 Factor the antilogarithm with the expression in which $10$ , that is the base, is included 
$\log _{ 10 } { \left( \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 2 } } \right) } + \log _{ 10 } { \left( \color{#FF6800}{ 2 } \right) }$
$\log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 2 } } \right) } + \log _{ 10 } { \left( 2 \right) }$
 Simplify the expression using $\log_{a}{a^{x}}=x\times\log_{a}{a}$
$\color{#FF6800}{ 2 } \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 10 } \right) } + \log _{ 10 } { \left( 2 \right) }$
$2 \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 10 } \right) } + \log _{ 10 } { \left( 2 \right) }$
 The logarithm is equal to 1 if a base is same as an antilogarithm 
$2 \times \color{#FF6800}{ 1 } + \log _{ 10 } { \left( 2 \right) }$
$2 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } + \log _{ 10 } { \left( 2 \right) }$
 Multiplying any number by 1 does not change the value 
$\color{#FF6800}{ 2 } + \log _{ 10 } { \left( 2 \right) }$
$2.3010$
Use the common log table to find the value in next
$\log _{ 10 } { \left( \color{#FF6800}{ 200 } \right) }$
 Rewrite in the scientific numeral system 
$\log _{ 10 } { \left( \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 2 } } \right) }$
$\log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 2 } } \right) }$
 Simplify the expression using $\log_{a}{x\times y}=\log_{a}{x}+\log_{a}{y}$
$\log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 2 } \right) } \color{#FF6800}{ + } \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 2 } } \right) }$
$\log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 2 } \right) } + \log _{ 10 } { \left( 10 ^ { 2 } \right) }$
 Find the value of $\log _{ 10 } { \left( 2 \right) }$ through the common log table 
$\color{#FF6800}{ 0.3010 } + \log _{ 10 } { \left( 10 ^ { 2 } \right) }$
$0.3010 + \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 2 } } \right) }$
 Simplify the expression using $\log_{a}{a^{x}}=x$
$0.3010 + \color{#FF6800}{ 2 }$
$\color{#FF6800}{ 0.3010 } \color{#FF6800}{ + } \color{#FF6800}{ 2 }$
 Add $0.3010$ and $2$
$\color{#FF6800}{ 2.3010 }$
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