What is 10log_{10}((50*10^{-3})/(1*10^{-6)}) ?

The solution to 10log_{10}((50*10^{-3})/(1*10^{-6)}) is 10(-log_{10}(20)+6)

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simplify 10log_{10}((5010^{-3})/(110^{-6)})

simplify

10 lo g_{10} (\frac{50 \cdot 1 0 ^{- 3}}{1 \cdot 1 0 ^{- 6}})

10 (- lo g_{10} (20) + 6)

Decimal Notation

46.98970 \dots

Solution steps

10 lo g_{10} (\frac{50 \cdot 1 0 ^{- 3}}{1 \cdot 1 0 ^{- 6}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{50 \cdot 1 0 ^{- 3}}{1 \cdot 1 0 ^{- 6}}) = lo g_{10} (50 \cdot 1 0^{- 3}) - lo g_{10} (1 \cdot 1 0^{- 6})

= 10 (lo g_{10} (1 0^{- 3} \cdot 50) - lo g_{10} (1 0^{- 6} \cdot 1))

Multiply

50 \cdot 1 0^{- 3} : \frac{1}{20}

= 10 (lo g_{10} (\frac{1}{20}) - lo g_{10} (1 0^{- 6} \cdot 1))

Simplify

1 \cdot 1 0^{- 6} : \frac{1}{1 0 ^{6}}

= 10 (lo g_{10} (\frac{1}{20}) - lo g_{10} (\frac{1}{1 0 ^{6}}))

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= 10 (- lo g_{10} (20) - lo g_{10} (\frac{1}{1 0 ^{6}}))

lo g_{10} (\frac{1}{1 0 ^{6}}) = - 6

= 10 (- lo g_{10} (20) - (- 6))

Apply rule

- (- a) = a

= 10 (- lo g_{10} (20) + 6)

4 ln (x) + ln (y)

ln (x) + ln (x^{2}) - 6

- \frac{1}{6} ln (12) + \frac{1}{6} ln (6)

\frac{1}{2} ln (3 e^{2 x})

ln (\frac{e ^{3 x} x}{sin ( 7 x )})

What is 10log_{10}((50*10^{-3})/(1*10^{-6)}) ?
The solution to 10log_{10}((50*10^{-3})/(1*10^{-6)}) is 10(-log_{10}(20)+6)