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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{e} (10 e)

ln (4 e^{(2)})

12 lo g_{5} (x) - 6 lo g_{5} (y)

ln (\frac{2}{24})

- lo g_{10} (4 \cdot 1 0^{- 12})

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