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Popular >

simplify ln((e^x)/(1+e^x))

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{x}) = x ln (e)

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

x ln (e) = x

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

Popular Examples

simplify log_{10}((5x)/y)simplify

lo g_{10} (\frac{5 x}{y})

domain of f(x)=ln(x)-3[ln(x-7)+ln(x+7)]domain

f (x) = ln (x) - 3 [ln (x - 7) + ln (x + 7)]

simplify ln((e^5)/9)simplify

ln (\frac{e ^{5}}{9})

expand log_{b}((x^3y)/(z^5))expand

lo g_{b} (\frac{x ^{3} y}{z ^{5}})

expand log_{8}(a^6b^5)expand

lo g_{8} (a^{6} b^{5})

Frequently Asked Questions (FAQ)

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