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

Question

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.

Answer 1

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.

Answer 2

Hint: $$\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)$$

Answer 3

Hint

Apply properties of logarithms to get

$$\ln 4x-\ln (x+7)=\ln \frac{4x}{x+7}.$$