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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{10} (x^{2} y^{5} z)

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

ln (7) + 4 ln (4)

- lo g_{10} (6.3 \cdot 1 0^{- 9})

6 ln (c) + 6 ln (x)

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