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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (e^{- x} + 1)

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

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

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Frequently Asked Questions (FAQ)

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