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horrorfan [7]
3 years ago
13

Which expression is equivalent to Left-bracket log 9 + one-half log x + log (x cubed + 4) Right-bracket minus log 6? log StartFr

action 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
Mathematics
1 answer:
dybincka [34]3 years ago
3 0

Answer:

  \log{\dfrac{3\sqrt{x}(x^3+4)}{2}}

Step-by-step explanation:

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

__

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)

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