Suppose we want to evaluate
$$\lim_{x \to 0} \; x \log (x)$$
If we write this in the form $x/(1/\log(x))$, then l'Hôpital's rule does not work, but if we write it as $\log(x)/(1/x)$, it does. Is there any sort of general guideline to choosing the numerator and denominator?