What is expand ln((e^x)/(1+e^x)) ?

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

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

expand

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

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)

2 [ln (x) + ln (x + 1) - ln (x - 1)]

lo g_{3} (\frac{16}{z})

lo g_{10} (4 x^{2} y)

ln^{4} (a x)

lo g_{10} (\frac{y ^{3}}{2 x})

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