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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{8} (\frac{4 5}{6})

6 ln (x) + 4 ln (y) - 3 ln (z)

lo g_{10} (\frac{a ^{2} ab}{( ab ) ^{2}})

2 lo g_{10} (x) - 8 lo g_{10} (y)

- lo g_{10} (2 \cdot 1 0^{- 2})

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