Answer
$x = 3.303$
Work Step by Step
$\ln(x) + \ln(x-3) = 0$
$ln(x(x-3)) = 0$
$ln(x^{2}- 3x) = 0$
$x^{2} - 3x = e^{0}$
$x^{2} - 3x = 1$
$x^{2} - 3x - 1 = 0$
Use the quadratic formula to find $x$
$= \frac{-(-3) ±\sqrt {(-3)^{2}-4(1)(-1)}}{2(1)}$
$= \frac{3 ±\sqrt {9+4}}{2}$
$= \frac{3 ±\sqrt {13}}{2}$
$x = 3.303, -0.303$
Since $x \gt 0$, then the only answer is $x = 3.303$
