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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)

Popular Examples

simplify log_{10}(1/(10^{3456)})simplify

lo g_{10} (\frac{1}{1 0 ^{3456}})

simplify ln(3/16)simplify

ln (\frac{3}{16})

simplify 1/4 log_{10}(0.485)+1/3 log_{10}(0.36)simplify

\frac{1}{4} lo g_{10} (0.485) + \frac{1}{3} lo g_{10} (0.36)

expand ln((2x)/(y^4))expand

ln (\frac{2 x}{y ^{4}})

simplify ln(2)+ln(x+1)-(ln(4x+7))/3 simplify

ln (2) + ln (x + 1) - \frac{ln ( 4 x + 7 )}{3}

Frequently Asked Questions (FAQ)

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