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

The solution to 10log_{10}((10^{-8})/(10^{-12)}) is 40

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simplify 10log_{10}((10^{-8})/(10^{-12)})

simplify

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

40

Solution steps

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

Apply log rule:

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

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

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

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

= 10 \cdot 4

Multiply the numbers:

10 \cdot 4 = 40

= 40

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What is 10log_{10}((10^{-8})/(10^{-12)}) ?
The solution to 10log_{10}((10^{-8})/(10^{-12)}) is 40