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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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)

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

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)

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

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

lo g_{y} (\frac{z}{x})

ln (\frac{x}{x ^{2}})

ln (x + 6) - ln (7)

- lo g_{10} (1.8 \cdot 1 0^{- 4} (\frac{0.025}{0.0375}))

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