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Formula
Calculate the value
Answer
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$$\log _{ 10 } { \left( 100 \right) }$$
$2$
Calculate the value
$\log _{ 10 } { \left( \color{#FF6800}{ 100 } \right) }$
$ $ Write the number in exponential form with base $ 10$
$\log _{ 10 } { \left( \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 2 } } \right) }$
$\log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 2 } } \right) }$
$ $ Simplify the expression using $ \log_{a}{a^{x}}=x\times\log_{a}{a}$
$\color{#FF6800}{ 2 } \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 10 } \right) }$
$2 \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 10 } \right) }$
$ $ 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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