What is 10log_{10}((8*10^{-4})/(1*10^{-12)}) ?

The solution to 10log_{10}((8*10^{-4})/(1*10^{-12)}) is 10(-log_{10}(1250)+12)

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simplify 10log_{10}((810^{-4})/(110^{-12)})

simplify

10 lo g_{10} (\frac{8 \cdot 1 0 ^{- 4}}{1 \cdot 1 0 ^{- 12}})

10 (- lo g_{10} (1250) + 12)

Decimal Notation

89.03089 \dots

Solution steps

10 lo g_{10} (\frac{8 \cdot 1 0 ^{- 4}}{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{8 \cdot 1 0 ^{- 4}}{1 \cdot 1 0 ^{- 12}}) = lo g_{10} (8 \cdot 1 0^{- 4}) - lo g_{10} (1 \cdot 1 0^{- 12})

= 10 (lo g_{10} (1 0^{- 4} \cdot 8) - lo g_{10} (1 0^{- 12} \cdot 1))

Multiply

8 \cdot 1 0^{- 4} : \frac{1}{1250}

= 10 (lo g_{10} (\frac{1}{1250}) - 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}{1250}) - 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} (1250) - lo g_{10} (\frac{1}{1 0 ^{12}}))

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

= 10 (- lo g_{10} (1250) - (- 12))

Apply rule

- (- a) = a

= 10 (- lo g_{10} (1250) + 12)

lo g_{10} (\frac{x + 10}{10 x ^{2}})

ln (\frac{a ^{2} b ^{4}}{c ^{8}})

ln (\frac{47}{50}) + (0.085)

ln (\frac{( x + 2 ) ^{7}}{x ^{5}})

ln (4 e^{- \frac{6}{100} t}) - ln (0.03 t)

What is 10log_{10}((8*10^{-4})/(1*10^{-12)}) ?
The solution to 10log_{10}((8*10^{-4})/(1*10^{-12)}) is 10(-log_{10}(1250)+12)