What is 10*log_{10}((5*10^{-6})/(1*10^{-12)}) ?

The solution to 10*log_{10}((5*10^{-6})/(1*10^{-12)}) is 10(-log_{10}(200000)+12)

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simplify 10log_{10}((510^{-6})/(1*10^{-12)})

simplify

10 \cdot lo g_{10} (\frac{5 \cdot 1 0 ^{- 6}}{1 \cdot 1 0 ^{- 12}})

10 (- lo g_{10} (200000) + 12)

Decimal

66.98970 \dots

Solution steps

10 lo g_{10} (\frac{5 \cdot 1 0 ^{- 6}}{1 \cdot 1 0 ^{- 12}})

Apply log rule:

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

lo g_{10} (\frac{5 \cdot 1 0 ^{- 6}}{1 \cdot 1 0 ^{- 12}}) = lo g_{10} (5 \cdot 1 0^{- 6}) - lo g_{10} (1 \cdot 1 0^{- 12})

= 10 (lo g_{10} (1 0^{- 6} \cdot 5) - lo g_{10} (1 0^{- 12} \cdot 1))

Multiply

5 \cdot 1 0^{- 6} : \frac{1}{200000}

= 10 (lo g_{10} (\frac{1}{200000}) - lo g_{10} (1 0^{- 12} \cdot 1))

Simplify

1 \cdot 1 0^{- 12} : \frac{1}{1 0 ^{12}}

= 10 (lo g_{10} (\frac{1}{200000}) - lo g_{10} (\frac{1}{1 0 ^{12}}))

Apply log rule:

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

= 10 (- lo g_{10} (200000) - lo g_{10} (\frac{1}{1 0 ^{12}}))

lo g_{10} (\frac{1}{1 0 ^{12}}) = - 12

= 10 (- lo g_{10} (200000) - (- 12))

Apply rule

- (- a) = a

= 10 (- lo g_{10} (200000) + 12)

100 + 20 \cdot ln (\frac{65}{65 - 23})

ln (\frac{4}{9}) \cdot \frac{20}{ln ( \frac{4}{11} )}

ln ((- 2.772)^{19.764})

\frac{1}{2} ln ∣ 2 (12) + 1 ∣ + 2 ln ∣ 12 - 1 ∣

ln (x sin (x) d x)

What is 10*log_{10}((5*10^{-6})/(1*10^{-12)}) ?
The solution to 10*log_{10}((5*10^{-6})/(1*10^{-12)}) is 10(-log_{10}(200000)+12)