# Calculator search results

Formula
Calculate the value
$\log {\left( \dfrac{ 1 }{ 50 } \right)} + \log {\left( \dfrac{ 1 }{ 20 } \right)}$
$- 3$
Calculate the value
$\log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ \dfrac { 1 } { 50 } } \right) } + \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ \dfrac { 1 } { 20 } } \right) }$
 Calculate addition of logarithm 
$\log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ \dfrac { 1 } { 1000 } } \right) }$
$\log _{ 10 } { \left( \dfrac { \color{#FF6800}{ 1 } } { 1000 } \right) }$
 Since the logarithm of antilogarithm numbers and numerator is 1 as the fraction, add minus to the logarithm and take reciprocal to antilogarithm numbers 
$\color{#FF6800}{ - } \log _{ 10 } { \left( \color{#FF6800}{ 1000 } \right) }$
$- \log _{ 10 } { \left( \color{#FF6800}{ 1000 } \right) }$
 Write the number in exponential form with base $10$
$- \log _{ 10 } { \left( \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 3 } } \right) }$
$- \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 10 } ^ { \color{#FF6800}{ 3 } } \right) }$
 Simplify the expression using $\log_{a}{a^{x}}=x\times\log_{a}{a}$
$- \left ( \color{#FF6800}{ 3 } \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 10 } \right) } \right )$
$- \left ( 3 \log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 10 } \right) } \right )$
 The logarithm is equal to 1 if a base is same as an antilogarithm 
$- \left ( 3 \times \color{#FF6800}{ 1 } \right )$
$- \left ( 3 \color{#FF6800}{ \times } \color{#FF6800}{ 1 } \right )$
 Multiplying any number by 1 does not change the value 
$- \color{#FF6800}{ 3 }$
Solution search results