What is 3log_{2}(A)+5log_{2}(B)-2log_{2}(C) ?

The solution to 3log_{2}(A)+5log_{2}(B)-2log_{2}(C) is log_{2}((A^3B^5)/(C^2))

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simplify 3log_{2}(A)+5log_{2}(B)-2log_{2}(C)

simplify

3 lo g_{2} (A) + 5 lo g_{2} (B) - 2 lo g_{2} (C)

lo g_{2} (\frac{A ^{3} B ^{5}}{C ^{2}})

Solution steps

3 lo g_{2} (A) + 5 lo g_{2} (B) - 2 lo g_{2} (C)

Apply log rule:

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

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

= lo g_{2} (A^{3}) + 5 lo g_{2} (B) - 2 lo g_{2} (C)

Apply log rule:

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

5 lo g_{2} (B) = lo g_{2} (B^{5})

= lo g_{2} (A^{3}) + lo g_{2} (B^{5}) - 2 lo g_{2} (C)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{2} (A^{3}) + lo g_{2} (B^{5}) = lo g_{2} (A^{3} B^{5})

= lo g_{2} (A^{3} B^{5}) - 2 lo g_{2} (C)

Apply log rule:

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

2 lo g_{2} (C) = lo g_{2} (C^{2})

= lo g_{2} (A^{3} B^{5}) - lo g_{2} (C^{2})

Apply log rule:

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

lo g_{2} (A^{3} B^{5}) - lo g_{2} (C^{2}) = lo g_{2} (\frac{A ^{3} B ^{5}}{C ^{2}})

= lo g_{2} (\frac{A ^{3} B ^{5}}{C ^{2}})

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What is 3log_{2}(A)+5log_{2}(B)-2log_{2}(C) ?
The solution to 3log_{2}(A)+5log_{2}(B)-2log_{2}(C) is log_{2}((A^3B^5)/(C^2))