# Question on using L'Hopital's rule for this problem?

I'm doing some practice questions and I've encountered a wall. The question is:

Find the limit of the function $(\ln4x-\ln(x+7))$ as $x \rightarrow \infty$.

the indeterminate form is $\infty-\infty$, so I'm not sure how to advance from here. I think I would like $f(x)/g(x)$ form, but I'm not sure how to do that in this situation. Can you give me a hint in the right direction?

I certainly don't want the answer.

• What is $\ln(a)-\ln(b)$? – Kitegi Mar 29 '15 at 22:24

HINT: $$\ln4x -\ln{(x+7)}=\ln\frac{4x}{ x+7}$$ from the properties of the logarithm.
Evaluate $\displaystyle \frac{4x}{x+7}$ and take the logarithm of your answer.
• Actually it's $ln ( \frac{4x}{x+7} ). – Patrick Mar 29 '15 at 22:21 • i.e. the log of the entire expression. – Patrick Mar 29 '15 at 22:21 • Apologies edited now. Can we delete these comments? – Permian Mar 29 '15 at 22:26 • I got the right answer. If you didn't answer, I wouldn't have known to evaluate the inside of the log first. Thank you. – NewbieNick Mar 31 '15 at 2:47 Hint: $$\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)$$ • Don't forget to use \ln instead of ln to produce the proper non-italic text, e.g.$\ln$vs$ln\$. – MathMajor Mar 29 '15 at 22:30
$$\ln 4x-\ln (x+7)=\ln \frac{4x}{x+7}.$$