What is 2log_{3}(A)-3log_{3}(B) ?

The solution to 2log_{3}(A)-3log_{3}(B) is log_{3}((A^2)/(B^3))

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simplify 2log_{3}(A)-3log_{3}(B)

simplify

2 lo g_{3} (A) - 3 lo g_{3} (B)

lo g_{3} (\frac{A ^{2}}{B ^{3}})

Solution steps

2 lo g_{3} (A) - 3 lo g_{3} (B)

Apply log rule:

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

2 lo g_{3} (A) = lo g_{3} (A^{2})

= lo g_{3} (A^{2}) - 3 lo g_{3} (B)

Apply log rule:

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

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

= lo g_{3} (A^{2}) - lo g_{3} (B^{3})

Apply log rule:

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

lo g_{3} (A^{2}) - lo g_{3} (B^{3}) = lo g_{3} (\frac{A ^{2}}{B ^{3}})

= lo g_{3} (\frac{A ^{2}}{B ^{3}})

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What is 2log_{3}(A)-3log_{3}(B) ?
The solution to 2log_{3}(A)-3log_{3}(B) is log_{3}((A^2)/(B^3))