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:
$\log_5[(x+3)(x-1)] \ ...(1)$
Since, $\log_m{n} = 1 $ gives: $m^{(1)}=n$, then we have:
$\log (x+3)(x-1)= 5^1$
$\log (x^2+2x-3)=5$
or, $x^2+2x-8=0$
This is a quadratic equation; thus by factoring, it will become:
$(x+4)(x-2)=0$
By the zero product property, we have: $x=2$ and $x=-4$
Since the domain of the variable is $x \gt 0$, we cannot accept the value of $x=-4$
Thus, our answer is: $x= 2$
