Answer
$x= -6$
Work Step by Step
Apply the logarithmic property:
$\log_a M+\log_a N = \log_a (MN)$ and rearrange the given expression to obtain:
$\log_2[(x+7)(x+8)] \ ...(1)$
Since, $\log_m{n} = 1 $ gives: $m^{(1)}=n$, then we have:
$\log (x^2+15x+5)= 2^1$
or, $x^2+15x+54=0$
or, $(x+9)(x+6)=0$
By the zero product property, we have: $x=-9$ and $x=-6$
Since, the domain of the variable is $x \gt 0$, we cannot accept the value of $x=-9$
Thus, our answer is: $x= -6$
