Symbol

# Calculator search results

Formula
Calculate the value
Find the value of the common log
$\log_{ 10 } {\left( \dfrac{ 1 }{ 1000 } \right)}$
$- 3$
Calculate the value
$\log _{ 10 } { \left( \dfrac { \color{#FF6800}{ 1 } } { 1000 } \right) }$
 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 
$- \color{#FF6800}{ 3 }$
$- \log _{ 10 } { \left( 1000 \right) }$
Use the common log table to find the value in next
$\log _{ 10 } { \left( \color{#FF6800}{ \dfrac { 1 } { 1000 } } \right) }$
 If the antilogarithm numbers number of logarithm is a fraction, convert it to two logarithms' subtraction with antilogarithm number of the numerator and denominator 
$\log _{ 10 } { \left( \color{#FF6800}{ 1 } \right) } - \log _{ 10 } { \left( \color{#FF6800}{ 1000 } \right) }$
$\log _{ \color{#FF6800}{ 10 } } { \left( \color{#FF6800}{ 1 } \right) } - \log _{ 10 } { \left( 1000 \right) }$
 Antilogarithm value with the logarithm of 1 is equal to 0 
$\color{#FF6800}{ 0 } - \log _{ 10 } { \left( 1000 \right) }$
$\color{#FF6800}{ 0 } - \log _{ 10 } { \left( 1000 \right) }$
 0 does not change when you add or subtract 
$- \log _{ 10 } { \left( 1000 \right) }$
Have you found the solution you wanted?
Try again
Try more features at Qanda!
Search by problem image
Ask 1:1 question to TOP class teachers
AI recommend problems and video lecture