Determine if the following functions grow faster, slower, or at the same rate as the function $\ln x$ as $x \to \infty$.
a. $\log_6 x$
e. $6x$
b. $\ln 3x$
f. $4 \ln x$
c. $\ln \sqrt{x}$
d. $\sqrt{3x}$
g. $\frac{4}{x}$
h. $e^{3x}$
a. The function $\log_6 x$ grows
$\ln x$ as $x \to \infty$ because $\lim_{x \to \infty} \frac{\ln x}{\log_6 x} = $