What is ln(1/(sqrt(u^2+v^2))) ?

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

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simplify ln(1/(sqrt(u^2+v^2)))

simplify

ln (\frac{1}{u ^{2} + v ^{2}})

- ln (u^{2} + v^{2})

Solution steps

ln (\frac{1}{u ^{2} + v ^{2}})

Apply log rule:

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

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

= ln (1) - ln (u^{2} + v^{2})

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (u^{2} + v^{2})

0 - ln (u^{2} + v^{2}) = - ln (u^{2} + v^{2})

= - ln (u^{2} + v^{2})

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lo g_{2} (\frac{2 x ^{6}}{y})

lo g_{2} \frac{3 x ^{2}}{2 ( a y ^{5} )}

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