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.

Let $y = \lim_{x→\infty}(1+\frac{2}{x} )^{3x} $
$\log y = \lim_{x→\infty}(3x) ~~\log~(1+\frac{2}{x} ) $
$= \lim_{x→\infty} \frac{ \log~(1+\frac{2}{x} )}{\frac{1}{3x} }$
$= 0/0 $ form.
Differentiate numerator and denominator and get limit value as
$\log y = \lim_{x→\infty} {\frac {1} {(1+2/x)} }. (\frac {-2}{x^2}).(-\frac {x^2}{3})$
=$2/3$
Hence, $y=e^{2/3}$
