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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_{5}(6)+log_{5}(8)-log_{5}(12)simplify

lo g_{5} (6) + lo g_{5} (8) - lo g_{5} (12)

simplify log_{2}(x)+log_{2}(y)-log_{2}(z)simplify

lo g_{2} (x) + lo g_{2} (y) - lo g_{2} (z)

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lo g_{10} (\frac{y ^{7}}{x z ^{3}})

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lo g_{3} (6 x)

simplify ln(10/7)simplify

ln (\frac{10}{7})

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)