What is 3log_{5}(x+y)-2log_{5}(x-y) ?

The solution to 3log_{5}(x+y)-2log_{5}(x-y) is log_{5}(((x+y)^3)/((x-y)^2))

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simplify 3log_{5}(x+y)-2log_{5}(x-y)

simplify

3 lo g_{5} (x + y) - 2 lo g_{5} (x - y)

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

Solution steps

3 lo g_{5} (x + y) - 2 lo g_{5} (x - y)

Apply log rule:

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

3 lo g_{5} (x + y) = lo g_{5} ((x + y)^{3})

= lo g_{5} ((x + y)^{3}) - 2 lo g_{5} (x - y)

Apply log rule:

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

2 lo g_{5} (x - y) = lo g_{5} ((x - y)^{2})

= lo g_{5} ((x + y)^{3}) - lo g_{5} ((x - y)^{2})

Apply log rule:

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

lo g_{5} ((x + y)^{3}) - lo g_{5} ((x - y)^{2}) = lo g_{5} (\frac{( x + y ) ^{3}}{( x - y ) ^{2}})

= lo g_{5} (\frac{( x + y ) ^{3}}{( x - y ) ^{2}})

4 ln (\frac{1}{2})

ln (2 y) - ln (y)

2 ln (4) + 3 ln (x) - 4 ln (y)

5 lo g_{2} (k) - 8 lo g_{2} (m) + 10 lo g_{2} (n)

3 ln (A) - \frac{1}{2} [ln (B) + 2 ln (C^{2})]

What is 3log_{5}(x+y)-2log_{5}(x-y) ?
The solution to 3log_{5}(x+y)-2log_{5}(x-y) is log_{5}(((x+y)^3)/((x-y)^2))