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

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

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simplify 2log_{3}(x-y)-3log_{3}(m)

simplify

2 lo g_{3} (x - y) - 3 lo g_{3} (m)

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

Solution steps

2 lo g_{3} (x - y) - 3 lo g_{3} (m)

Apply log rule:

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

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

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

Apply log rule:

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

3 lo g_{3} (m) = lo g_{3} (m^{3})

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

Apply log rule:

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

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

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

ln (A) - ln (B)

ln (\frac{a}{b c})

ln (x) + ln (3 y)

ln (32)

ln (1) - ln (2 x)

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