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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

ln (\frac{1}{80})

ln (\frac{2 a}{b})

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

ln (\frac{52}{62})

ln (2.1 \cdot e^{4})

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