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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Popular Examples

simplify 2+log_{10}(x)+log_{10}(y)simplify

2 + lo g_{10} (x) + lo g_{10} (y)

simplify log_{10}(z/(x^7))simplify

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

simplify 2log_{10}(p)+5log_{10}(q)-log_{10}(r)simplify

2 lo g_{10} (p) + 5 lo g_{10} (q) - lo g_{10} (r)

simplify 1/2 log_{b}(x)+5log_{b}(y)-3log_{b}(x)simplify

\frac{1}{2} lo g_{b} (x) + 5 lo g_{b} (y) - 3 lo g_{b} (x)

simplify ln((x^5*(1-x)^{45})/(A^5B^{45)})simplify

ln (\frac{x ^{5} \cdot ( 1 - x ) ^{45}}{A ^{5} B ^{45}})

Frequently Asked Questions (FAQ)

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