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Popular >

simplify-ln(1/(1+e^θ))

Solution

simplify

- ln (\frac{1}{1 + e ^{θ}})

Solution

ln (e^{θ} + 1)

Solution steps

- ln (\frac{1}{1 + e ^{θ}})

Apply log rule:

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

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

= - (- ln (e^{θ} + 1) + ln (1))

Apply log rule:

lo g_{a} (1) = 0

= - (- ln (e^{θ} + 1) + 0)

Refine

= ln (e^{θ} + 1)

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Frequently Asked Questions (FAQ)

What is simplify-ln(1/(1+e^θ)) ?
The solution to simplify-ln(1/(1+e^θ)) is ln(e^θ+1)