Imagine I have this limit:
$$\lim_{x\to 0}\frac{\ln(1+2x)}x$$
Using the L'Hospital's rule the result is $2$.
Using this result is it possible to calculate
$$\lim_{n\to \infty}\ n\ln\bigg(1+\frac{4}{\sqrt{n}}\bigg) \quad ?$$
Sorry if this is an easy question, but many years have passed since I've learned calculus.