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

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

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

simplify

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

- 12 ln (10) - ln (2)

Decimal Notation

- 28.32416 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= - 12 lo g_{e} (10) - lo g_{e} (2)

Simplify

lo g_{e} (10) : ln (10)

= - 12 ln (10) - lo g_{e} (2)

Apply log rule:

lo g_{e} (x) = ln (x)

= - 12 ln (10) - ln (2)

lo g_{10} (x y^{7})

lo g_{b} (\frac{1}{21})

2 lo g_{4} (11) - 10 lo g_{4} (10)

3 ln (x) - ln (3 x) + ln (12 x^{2})

ln (x^{2}) - 2 ln (y)

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