What is ln((sqrt(1+x^2))/(1-x^2)) ?

The solution to ln((sqrt(1+x^2))/(1-x^2)) is ln(sqrt(1+x^2))-ln(1-x^2)

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simplify ln((sqrt(1+x^2))/(1-x^2))

simplify

ln (\frac{1 + x ^{2}}{1 - x ^{2}})

ln (1 + x^{2}) - ln (1 - x^{2})

Solution steps

ln (\frac{1 + x ^{2}}{1 - x ^{2}})

Apply log rule:

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

ln (\frac{1 + x ^{2}}{1 - x ^{2}}) = ln (1 + x^{2}) - ln (1 - x^{2})

= ln (x^{2} + 1) - ln (- x^{2} + 1)

lo g_{10} (\frac{5 k}{n ^{3}})

ln (x^{y} \cdot (1 - x)^{n - y})

\frac{1}{5} ln ∣ x - 3 ∣ - \frac{1}{5} ln ∣ x + 2 ∣

lo g_{e} (\frac{2}{3} w)

What is ln((sqrt(1+x^2))/(1-x^2)) ?
The solution to ln((sqrt(1+x^2))/(1-x^2)) is ln(sqrt(1+x^2))-ln(1-x^2)