How to evaluate $\lim_{x \to \infty}\left(1 + \frac{2}{x}\right)^{3x}$ using L'Hôpital's rule? I'm stuck on how to evaluate the following using L'Hôpital's rule:
$$\lim_{x \to \infty}\left(1 + \frac{2}{x}\right)^{3x}$$
This is a problem that I encountered on Khan Academy and I attempted to understand it using the resources there.  Here are the tips given for the problem; the portion that I'm having trouble understanding is highlighted:

I also attempted to use this video  (screenshot following) to help; I understand the concepts in the video but it seems like there are some missing steps in the tips above.

I also attempted to use WolframAlpha's step-by-step solution but it was indecipherable to me.
Any help is greatly appreciated.

Generally when l'hospital is involved in a complex limit, you need to set the limit equal to y then apply ln to both sides. To obtain the indeterminite form you need to move a variable to the denominator. The problem usually proceeds smoothly from there.  When you do solve the limit remember that it is set to ln (y), so solving for y is the final step involved.
