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)

ln (6) + 2 ln (3)

ln (3) + 3 ln (4)

ln (4 \cdot e^{2 x})

ln (3) + 4 ln (x) + 5 ln (x^{2} + 8)

lo g_{10} (80) - 0.3 lo g_{10} (3)

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})