lHopitals $ \lim_{x\rightarrow \infty} \; (\ln x)^{3 x} $? $ \displaystyle \lim_{x\rightarrow \infty} \; (\ln x)^{3 x} =$ ?
Okay, so what do I do with that power? I need to rewrite the term as fractions. How?
If it was the inner function that's in the power of something: $\ln x^{\frac{1}{3 x}}$ then I'd just simply rewritten it as $\frac{1}{3x} \cdot \ln x = \frac{\ln x}{3x}$

Why l'Hospital? $\ln x\to+\infty$ as $x\to+\infty$ and $3x\to+\infty$ as $x\to+\infty$. So, you have a limit of type 
$$
(+\infty)^{+\infty}=+\infty.
$$
