What is log_{10}((x^2+y^2)/((x-y)^3)) ?

The solution to log_{10}((x^2+y^2)/((x-y)^3)) is log_{10}(x^2+y^2)-3log_{10}(x-y)

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simplify log_{10}((x^2+y^2)/((x-y)^3))

simplify

lo g_{10} (\frac{x ^{2} + y ^{2}}{( x - y ) ^{3}})

lo g_{10} (x^{2} + y^{2}) - 3 lo g_{10} (x - y)

Solution steps

lo g_{10} (\frac{x ^{2} + y ^{2}}{( x - y ) ^{3}})

Apply log rule:

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

lo g_{10} (\frac{x ^{2} + y ^{2}}{( x - y ) ^{3}}) = lo g_{10} (x^{2} + y^{2}) - lo g_{10} ((x - y)^{3})

= lo g_{10} (x^{2} + y^{2}) - lo g_{10} ((x - y)^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} ((x - y)^{3}) = 3 lo g_{10} (x - y)

= lo g_{10} (x^{2} + y^{2}) - 3 lo g_{10} (x - y)

ln (\frac{- 4.15 + 8.05}{31.8})

- (\frac{17}{30}) lo g_{2} (\frac{17}{30}) - (\frac{13}{30}) lo g_{2} (\frac{13}{30})

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

lo g_{10} (\frac{y}{5})

2^{0} ln (2) - 3^{0} ln (3)

What is log_{10}((x^2+y^2)/((x-y)^3)) ?
The solution to log_{10}((x^2+y^2)/((x-y)^3)) is log_{10}(x^2+y^2)-3log_{10}(x-y)