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Formula
Calculate the value
Answer
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$\log_{ \left( \frac{ 1 }{ 2 } \right) } {\left( \dfrac{ 1 }{ 4 } \right)}$
$2$
Calculate the value
$\log _{ \color{#FF6800}{ \frac { 1 } { 2 } } } { \left( \dfrac { 1 } { 4 } \right) }$
$ $ Since the bottom of a logarithm is a fraction with a numerator of 1, put a minus to the logarithm and take an inverse number for the bottom $ $
$\color{#FF6800}{ - } \log _{ \color{#FF6800}{ 2 } } { \left( \dfrac { 1 } { 4 } \right) }$
$- \log _{ 2 } { \left( \dfrac { \color{#FF6800}{ 1 } } { 4 } \right) }$
$ $ Since the logarithm of antilogarithm numbers and numerator is 1 as the fraction, add minus to the logarithm and take reciprocal to antilogarithm numbers $ $
$- \left ( \color{#FF6800}{ - } \log _{ 2 } { \left( \color{#FF6800}{ 4 } \right) } \right )$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ - } \log _{ 2 } { \left( 4 \right) } \right )$
$ $ Simplify Minus $ $
$\log _{ 2 } { \left( 4 \right) }$
$\log _{ 2 } { \left( \color{#FF6800}{ 4 } \right) }$
$ $ Write the number in exponential form with base $ 2$
$\log _{ 2 } { \left( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \right) }$
$\log _{ \color{#FF6800}{ 2 } } { \left( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } \right) }$
$ $ Simplify the expression using $ \log_{a}{a^{x}}=x\times\log_{a}{a}$
$\color{#FF6800}{ 2 } \log _{ \color{#FF6800}{ 2 } } { \left( \color{#FF6800}{ 2 } \right) }$
$2 \log _{ \color{#FF6800}{ 2 } } { \left( \color{#FF6800}{ 2 } \right) }$
$ $ 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 $ $
$\color{#FF6800}{ 2 }$
Solution search results
search-thumbnail-If the sum of two consecutive 
numbers is $45$ and one number is $X$ 
.This statement in the form of 
equation $1s:$ 
$\left(1$ Point) $\right)$ 
$○5x+1$ $1eft\left(x+1$ $r1gnt\right)=45s$ 
$○sx+1ef\left(x+2$ $r1gnt\right)=145s$ 
$sx+1x=45s$
7th-9th grade
Algebra
search-thumbnail-Which of the following rational numbers are 
equivalent? 
$0Ptionsy$ 
A \frac{5}{6}, \frac{30}{36} 
B $s\sqrt{rac\left(} -2\right)\left(3\right)\sqrt{1rac} \sqrt{4\right)16\right)4} $ 
C $s\sqrt{11aC\left(} -4\right)1-7b,\sqrt{1rac\left(16\sqrt{35\right)9} } $ 
D \frac{1}{2},\frac{3}{8}
7th-9th grade
Other
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