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Popular >

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

Solution

simplify

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

Solution

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

+1

Decimal Notation

- 0.31326 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (1) = 0

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

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= 0 - ln (\frac{1}{e} + 1)

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

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

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Frequently Asked Questions (FAQ)

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