Answer:
log [ (3/2) *[tex]\sqrt{x}[/tex] * ([tex]x^{3}[/tex] + 4) ] = ( log 9 + 1/2 log x + log (x cubed + 4) - log 6 )
Step-by-step explanation:
I do not see answer choices, but I will simplify this expression.
( log 9 + 1/2 log x + log (x cubed + 4) - log 6 )
= log 9 - log 6 + 1/2 log x + log (x cubed + 4)
= log (9/6) + 1/2 log x + log (x cubed + 4),
I simply used the Quotient Rule for Logs
= log (9/6) + 1/2 log x + log (x cubed + 4),
= log (3/2) + 1/2 log x + log (x cubed + 4),
= log (3/2) + log x^(1/2) + log (x cubed + 4),
Power Rule for logs
= log (3/2) + log x^(1/2) + log (x cubed + 4),
= log ( (3/2)* x^(1/2) * (x cubed + 4) )
Applying Product Rule for Logs
= log ( (3/2)* x^(1/2) * (x cubed + 4) )
= log [ (3/2) *[tex]\sqrt{x}[/tex] * ([tex]x^{3}[/tex] + 4) ]
