Answer
$x= -2$
Work Step by Step
Apply the logarithmic property:
$\log_a M+\log_a N = \log_a (MN)$
and rearrange the given expression to obtain:
$\log_8[(x+6)(x+4)] \ ...(1)$
Since, $\log_m{n} = 1 $ gives: $m^{(1)}=n$, then we have:
$\log (x+6)(x+4)= 8^1$
$\log (x^2+10x+24)= 8$
or, $x^2+10x+16=0$
This is a quadratic equation; thus by factoring it will become:
$(x+8)(x+2)=0$
By the zero product property, we have: $x=-2$ and $x=-8$
Since the domain of the variable is $x \gt -4$, we cannot accept the value of $x=-8$
Thus, our answer is: $x= -2$
