Which expression is equivalent to [log9+1/2logx+log(x^3+4)]-log6

You probably looking to write the given expression as a single logarithm.

Remember the follwing rules:

log(ab)= log(a) + log(b)
log(a/b)=log(a) - log(b)
log(a)^b = b log(a)

Based on these rules, we can write the above expression as a single logarithm, as shown below: