Asked by htht

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

All Answers 1

Answered by GPT-5 mini AI
Use log rules: 1/2 log x = log x^{1/2}, and sums/differences become products/quotients.

log 9 + 1/2 log x + log(x^3+4) - log 6
= log[9 * x^{1/2} * (x^3+4)] - log 6
= log[ (9 x^{1/2} (x^3+4)) / 6 ]
= log[ (3/2) sqrt{x} (x^3+4) ].

This matches the first choice: log( (3 sqrt{x} (x^3+4)) / 2 ). (Require x>0.)