Limit of $\ln(x-a)$ and $\ln(x+a)$ where is a positive number.

Question

I have successfully found the limit of $\ln(x)$ as $x$ goes to infinity and minus infitiry. They are infinity and undefined, respectfully.

I understand that when we look for the limit of $\ln(x+a)$ or $\ln(x-a)$ the limits as x goes to infiity are the same, however I am having diffulity given $\ln(x+a)$ is not defined in some areas.

Thanks

Answer 1

$ln(x \pm a)$ is not defined when $x \le \mp a$. When $x \to \infty $, there is obviously no problem, and the limit goes to infinity as well (as long as $a \in \mathbb{R}$). When $x \to -\infty $, the limit is not defined properly.