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

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

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

simplify

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

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

Decimal Notation

- 430.55969 \dots

Solution steps

10 ln (\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)

ln (\frac{2 \cdot 1 0 ^{- 7}}{1 0 ^{- 12}}) = ln (2 \cdot 1 0^{- 7}) - ln (1 0^{- 12})

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

Apply log rule:

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

ln (1 0^{- 12}) = - 12 ln (10)

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

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2 lo g_{e} (x) - 4 lo g_{e} (\frac{1}{y}) - 3 lo g_{e} (x y)

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