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Formula
Calculate the value
Answer
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Find the value of the common log
Answer
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$\log_{ 10 } {\left( \dfrac{ 1 }{ 1000 } \right)}$
$- 3$
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 $ $
$- \log _{ 10 } { \left( 1000 \right) }$
Solution search results
search-thumbnail-$The\ reciprocal\\ 0+11) \left(\frac{2}
$8$ $\left(1$ Point) $1\right)$ The\ reciprocal\\ $0+11\right)$ \left(\frac{2} $c\left(2\right)$ {5}\right)^0\ $\right)$ \ $1111s\right)$ $S$ $S1S$ $s3S$ $S4S$ $s2S$
7th-9th grade
Other
Search count: 4,895
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search-thumbnail-(int|imits -0a1(1-\timesn_{2}{)_{3}}^{n}
$\left(int|imits$ $-0a1\left(1-\times n_{2}{\right)_{3}}^{n}$ $x^{A}3dx=7\right)$ $\left($ $frac\left(1\right)\left(40\right)\right)$ $\left($ $\left(troc\left(1\right)\left(35\right)\right)$ $\left(troc\left(1\right)\left(30\right)\right)$ $\left(tr0c\left(1\right)\left(25\right)\right)$
Calculus
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search-thumbnail-Which of the following rational numbers are
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
Search count: 5,909
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search-thumbnail-In the following problem a,b, b,and represent REAL NUMBERS.
In the following problem $a,b,$ b,and c represent REAL NUMBERS. The derivative of $g\left(x\right)=log _{a}\left(bx\right)+cx^{2}is$ $○$ $g^{1}\left(x\right)=\right)dfrac\left(b\right)log _{-}a\left(bx\right)\right)\left(N1n$ $a\right)+2cx1\right)$ $○$ $\left(g\left(x\right)=\right)dtracb$ $loga\left(bx\right)+2c\times \right)Nln$ a}\) $○$ $g^{'}\left(x\right)=\left(dfraC\left(a\right)log _{-}a\left(bx\right)\right)\left(ln$ $\right)+2c\times 1\right)\right)$ $○$ $g^{1}\left(x\right)=\left(dfrac\left(b$ $log _{-}a\left(bx\right)\right)\left(ln$ $a1\right)$ $○$ $\left(\left(g^{1}\left(x\right)=b$ $log _{-}a\left(bx\right)+2cx1\right)$ $○$ $g\left(x\right)=\left(dfrac\left(b$ $log _{-}a\left(bx\right)\right)\left(1ln$ $a|+2c1\right)$
Calculus
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