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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

0.1 ln (\frac{20 + 409}{3})

ln (\frac{x + 2}{x})

lo g_{10} (\frac{17 x}{y})

ln (3 x^{5} y)

\frac{1}{5} x^{5} (3 ln (2) + 2 ln (x))

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