After applying L'Hospital's Rule once, we have $\lim_{x \to \infty} \frac{\ln(x)}{3x}$. So, we still have an indeterminate limit of type $\frac{\infty}{\infty}$. We recall that L'Hospital's Rule can be applied repeatedly as needed, and we will do so here, applying the rule for a second time. To do so, we need to find additional derivatives.
The derivative of $\ln(x)$ with respect to x is
The derivative of $3x$ with respect to x is
