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Formula
Calculate the value
$\log {\left( \dfrac{ 1 }{ \sqrt{ x } } \right)}$
$- \dfrac { 1 } { 2 } \log _{ 10 } { \left( x \right) }$
Simplify the expression
$\log _{ 10 } { \left( \dfrac { \color{#FF6800}{ 1 } } { \sqrt{ x } } \right) }$
 Since the logarithm of antilogarithm numbers and numerator is 1 as the fraction, add minus to the logarithm and take reciprocal to antilogarithm numbers 
$\color{#FF6800}{ - } \log _{ 10 } { \left( \sqrt{ x } \right) }$
$- \log _{ 10 } { \left( \sqrt{ \color{#FF6800}{ x } } \right) }$
 Convert the square root of the antilogarithm number of the logarithm to the power 
$- \log _{ 10 } { \left( \color{#FF6800}{ x } ^ { \color{#FF6800}{ \frac { 1 } { 2 } } } \right) }$
$- \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ x } ^ { \color{#FF6800}{ \frac { 1 } { 2 } } } \right) }$
 Simplify the expression using $\log_{a}{b^{x}}=x\times\log_{a}{b}$
$- \left ( \color{#FF6800}{ \dfrac { 1 } { 2 } } \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ x } \right) } \right )$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ \dfrac { 1 } { 2 } } \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ x } \right) } \right )$
 Get rid of unnecessary parentheses 
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 1 } { 2 } } \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ x } \right) }$
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