Answer
$-\infty$
Work Step by Step
$$\lim_{x \to 0^{+}}\ln(\sin(x))=\ln(\lim_{x \to 0^{+}}(\sin(x))$$
Since $\lim_{x \to 0^{+}}(\sin(x))=0$ it follows:
$$\ln(\lim_{x \to 0^{+}}(\sin(x))=\lim_{x \to 0}\ln (x)=-\infty$$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.