Answer
$x = 12, 2$
$x \ne 2$, therefore $x = 12$
Work Step by Step
$\log_2(x-6) + \log_2 (x-4) - \log_2 x = 2$
$\log_2(x-6)(x-4) - \log_2 x = 2$
$\log_2 \frac{(x-6)(x-4)}{x} = 2$
$2^{2} = \frac{(x-6)(x-4)}{x}$
$\frac{(x-6)(x-4)}{x} = 4$
$(x-6)(x-4) = 4x$
$x(x-4)-6(x-4) = 4x$
$x^{2} - 4x - 6x + 24 - 4x = 0$
$x^{2} - 10x - 4x + 24 = 0$
$x^{2} - 14x + 24 = 0$
$x^{2} - 12x - 2x + 24 = 0$
$(x - 12)(x-2) = 0 $
$x = 12, 2$
$x \ne 2$, therefore $x = 12$
