Answer
$x = 4$
Work Step by Step
$\log_4 (2x+1) = \log_4 (x-3) + \log_4 (x+5)$
$\log_4 (2x+1) = \log_4 (x-3)(x+5)$
$2x + 1 = (x-3)(x+5)$
$2x + 1 = x(x+5) - 3(x+5)$
$2x + 1 = x^{2} + 5x - 3x - 15$
$2x + 1 = x^{2} + 2x - 15$
$x^{2} + 2x - 2x - 15 - 1 = 0$
$x^{2} -16 = 0$
$x^{2} = 16$
$x = ±4$
Since $x \ne -4$, then $x = 4$
