What is ln((-1)/2 e^{-2x}) ?

The solution to ln((-1)/2 e^{-2x}) is ln(-1)-ln(2)-2x

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simplify ln((-1)/2 e^{-2x})

simplify

ln (\frac{- 1}{2} e^{- 2 x})

ln (- 1) - ln (2) - 2 x

Solution steps

ln (\frac{- 1}{2} e^{- 2 x})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (\frac{- 1}{2} e^{- 2 x}) = ln (\frac{- 1}{2}) + ln (e^{- 2 x})

= ln (\frac{- 1}{2}) + ln (e^{- 2 x})

Apply log rule:

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

ln (e^{- 2 x}) = - 2 x ln (e)

= ln (\frac{- 1}{2}) - 2 x ln (e)

Apply log rule:

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

ln (\frac{- 1}{2}) = ln (- 1) - ln (2)

= ln (- 1) - ln (2) - 2 ln (e) x

2 x ln (e) = 2 x

= ln (- 1) - ln (2) - 2 x

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9 lo g_{10} (7) - 5 lo g_{10} (23)

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

What is ln((-1)/2 e^{-2x}) ?
The solution to ln((-1)/2 e^{-2x}) is ln(-1)-ln(2)-2x