Question

Which expression is equivalent to Left-bracket log 9 + one-half log x + log (x cubed + 4) Right-bracket minus log 6? log StartFraction 3 StartRoot x EndRoot (x cubed + 4) Over 2 EndFraction log StartFraction 3 StartRoot x EndRoot (3 x + 4) Over 2 EndFraction log StartFraction StartRoot 9 x (x cubed + 4) EndRoot Over 6 EndFraction StartFraction StartRoot log 9 x ( x cubed + 4) EndRoot Over 6 EndFraction

Answer 1

A

Explanation:

Just did it on edge2020

Answer 2

`\log{(3√(x)(x^3+4))/(2)}`

Explanation:

`\log{9}+(1)/(2)\log{x}+\log{(x^3+4)}-\log{6}=\log{\left(\frac{9x^{(1)/(2)}(x^3+4)}{6}\right)}\\\\=\boxed{\log{(3√(x)(x^3+4))/(2)}}\qquad\text{matches choice A}`

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The applicable rules of logarithms are ...

log(ab) = log(a) +log(b)

log(a/b) = log(a) -log(b)

log(a^b) = b·log(a)