Answer
$x=67$
Work Step by Step
Apply the logarithmic property:
$\log_a(\dfrac{M}{N}) = \log_a M-\log_a N$
and rearrange the given expression to obtain:
$\log_{4}[\dfrac{x^2 -9}{x+3}] =3$
Since $\log_m{n} = 1 $ gives: $m^{(1)}=n$, then we have:
$4^3=\dfrac{x^2-9}{x+3}$
$x^2-9=64 x+192$
or, $x^2-64x -201=0$
This is a quadratic equation; thus by factoring, it will become:
$(x+3)(x-67)=0$
By the zero product property, we have: $x=-3$ and $x=67$
Since the domain of the variable is $x \gt 0$, we cannot accept the value of $x=-3$
Thus, our answer is: $x=67$
