Answer
$-\infty$
Work Step by Step
Find the limit $\lim\limits_{x \to 3^{+}}ln(x^{2}-9)$
This is quadratic equation in the powers of 2.
Suppose, $n=\lim\limits_{x \to 3^{+}}(x^{2}-9)$
$=\lim\limits_{x \to 3^{+}}(x-3)(x+3)$
Thus, $n=0$
The limit of the natural logarithm of $x$ when $x$ approaches zero from the positive side (0+) is minus infinity. This implies
Hence, $\lim\limits_{x \to 3^{+}}ln(x^{2}-9)=-\infty$