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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (x^{2} + y^{2})

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

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

ln (e^{2} ln (e^{3}))

\frac{1}{2} (ln (x - 1) - ln (3))

\frac{1}{3} ln (\frac{5}{2})

3 lo g_{4} (x + 1) - lo g_{4} (x)

ln (x^{- 3}) + ln (x^{2})

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