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

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

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simplify 10log_{10}((210^{-2})/(10^{-12)})

simplify

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

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

Decimal Notation

- 136.98970 \dots

Solution steps

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

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

ln (\frac{4}{13})

lo g_{7} (\frac{14}{49}) - ln (2)

ln (2 c)

2 lo g_{b} (q) + 3 lo g_{b} (y)

ln (\frac{1}{x ^{2} + y ^{2}})

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