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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{a} ((x + y)^{3}) = 3 lo g_{a} (x + y)

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

Apply log rule:

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

lo g_{a} ((x - y)^{2}) = 2 lo g_{a} (x - y)

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

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\frac{1}{3} lo g_{10} (x) - lo g_{10} (5)

3 ln ∣ x ∣ - 2 ln ∣ x + 1 ∣

ln (a^{4} b^{7})

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