Answer
$x = \frac{11}{3}$
$x = 3.67$
Work Step by Step
$\ln (x-2) - \ln(x+3) = \ln(x-1) - \ln(x+7)$
$\ln \frac{x-2}{x+3} = \ln \frac{x-1}{x+7}$
$\frac{x-2}{x+3} = \frac{x-1}{x+7}$
$(x-2)(x+7) = (x-1)(x+3)$
$x(x+7) - 2(x+7) = x(x+3)-1(x+3)$
$x^{2} + 7x - 2x - 14 = x^{2} + 3x - x - 3$
$x^{2} + 5x - 14 = x^{2} + 2x - 3$
$x^{2} - x^{2} + 5x - 2x - 14 + 3 = 0$
$3x - 11 = 0$
$3x = 11$
$x = \frac{11}{3}$
$x = 3.67$
