What is 3/2 ln(x-y)-2ln(x^2+y^2) ?

The solution to 3/2 ln(x-y)-2ln(x^2+y^2) is ln(((x-y)^{3/2})/((x^2+y^2)^2))

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simplify 3/2 ln(x-y)-2ln(x^2+y^2)

simplify

\frac{3}{2} ln (x - y) - 2 ln (x^{2} + y^{2})

ln (\frac{( x - y ) ^{\frac{3}{2}}}{( x ^{2} + y ^{2} ) ^{2}})

Solution steps

\frac{3}{2} ln (x - y) - 2 ln (x^{2} + y^{2})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{3}{2} ln (x - y) = ln ((x - y)^{\frac{3}{2}})

= ln ((x - y)^{\frac{3}{2}}) - 2 ln (x^{2} + y^{2})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln ((x - y)^{\frac{3}{2}}) - ln ((x^{2} + y^{2})^{2})

Apply log rule:

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

ln ((x - y)^{\frac{3}{2}}) - ln ((x^{2} + y^{2})^{2}) = ln (\frac{( x - y ) ^{\frac{3}{2}}}{( x ^{2} + y ^{2} ) ^{2}})

= ln (\frac{( x - y ) ^{\frac{3}{2}}}{( x ^{2} + y ^{2} ) ^{2}})

\frac{9}{8} + \frac{8}{9}

x^{2} + x y - 2 y^{2}

x^{2} + 2 x + 4 = 9

n + n^{2}

2 x - 4 = 11 - x

What is 3/2 ln(x-y)-2ln(x^2+y^2) ?
The solution to 3/2 ln(x-y)-2ln(x^2+y^2) is ln(((x-y)^{3/2})/((x^2+y^2)^2))