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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

\frac{1}{3} lo g_{2} (3) + \frac{2}{3} lo g_{2} (\frac{3}{2})

lo g_{2} ((r + s) \cdot t)

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

\frac{1}{3} lo g_{3} (x^{6}) + \frac{1}{6} lo g_{3} (x^{6}) - \frac{1}{9} lo g_{3} (x)

2 ln (x - 1) + 3 ln (x + 1)

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