Answer
$x= -1$
Work Step by Step
Apply the logarithmic property:
$\log_a M+\log_a N = \log_a (MN)$
and rearrange the given expression to obtain:
$\log_6[(x+4)(x+3)] \ ...(1)$
Since, $\log_m{n} = 1 $ gives: $m^{(1)}=n$, then we have:
$\log (x+4)(x+3)= 6^1$
$\log (x^2+7x+12)= 6$
or, $x^2+7x+6=0$
This is a quadratic equation; thus by factoring, it will become:
$(x+6)(x+1)=0$
By the zero product property, we have: $x=-6$ and $x=-1$
Since, the domain of the variable is $x \gt -3$, we cannot accept the value of $x=-6$
Thus, our answer is: $x= -1$
