What is 10log_{10}((2*10^{-7})/(10^{-12)}) ?

The solution to 10log_{10}((2*10^{-7})/(10^{-12)}) is 10(log_{10}(2*10^{-7})--12log_{10}(10))

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simplify 10log_{10}((2*10^{-7})/(10^{-12)})

simplify

10 lo g_{10} (\frac{2 \cdot 1 0 ^{- 7}}{1 0 ^{- 12}})

10 (lo g_{10} (2 \cdot 1 0^{- 7}) - - 12 lo g_{10} (10))

Decimal Notation

- 186.98970 \dots

Solution steps

10 lo g_{10} (\frac{2 \cdot 1 0 ^{- 7}}{1 0 ^{- 12}})

Apply log rule:

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

lo g_{10} (\frac{2 \cdot 1 0 ^{- 7}}{1 0 ^{- 12}}) = lo g_{10} (2 \cdot 1 0^{- 7}) - lo g_{10} (1 0^{- 12})

= 10 (lo g_{10} (1 0^{- 7} \cdot 2) - lo g_{10} (1 0^{- 12}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 10 (lo g_{10} (2 \cdot 1 0^{- 7}) - - 12 lo g_{10} (10))

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What is 10log_{10}((2*10^{-7})/(10^{-12)}) ?
The solution to 10log_{10}((2*10^{-7})/(10^{-12)}) is 10(log_{10}(2*10^{-7})--12log_{10}(10))