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 do you hant to use l'hopital ? 
$$(\ln x)^{3x}=e^{3x\ln(\ln(x))}$$
and since $3x\ln(\ln(x))\underset{x\to \infty }{\longrightarrow }\infty $, 
$$\lim_{x\to\infty }(\ln x)^{3x}=\infty. $$
