Answer
$x = 8, -1$
$x \ne -1$, therefore $x = 8$
Work Step by Step
$\log_2 (x-3) + \log_2 x - \log_2 (x+2) = 2$
$\log_2 (x-3)(x) - \log_2(x+2) = 2$
$\log_2 \frac{x(x-3)}{x+2} = 2$
$2^{2} = \frac{x(x-3)}{x+2}$
$\frac{x(x-3)}{x+2} = 4$
$x(x-3) = 4(x+2)$
$x^{2} - 3x = 4x + 8$
$x^{2} - 3x - 4x - 8 = 0$
$x^{2} - 7x - 8 = 0$
$(x-8)(x+1) = 0$
$x = 8, -1$
$x \ne -1$, therefore $x = 8$
