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

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

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simplify ln(-2)-ln(1+e^{-2})

simplify

ln (- 2) - ln (1 + e^{- 2})

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

Solution steps

ln (- 2) - ln (1 + e^{- 2})

Apply log rule:

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

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

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

\frac{- 2}{1 + e ^{- 2}} = - \frac{2 e ^{2}}{e ^{2} + 1}

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

lo g_{10} (- 2 (1 + i))

ln (9 n) - 2 ln (3)

ln (\frac{170 + 273}{129.1 + 273})

ln (2 x + 6) - ln (7 x^{2} + 3)

ln (x (x + 4) (x + 8))

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