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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (x y) - ln (z)

29 ln (8) - 13 ln (4)

ln (\frac{5 x ^{6}}{11 y ^{7}})

- lo g_{10} (\frac{0.092}{0.085} \cdot 2.9 \cdot 1 0^{- 8})

ln (\frac{11}{15})

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