Answer
See proof
Work Step by Step
$$\lim_{x \to \infty}\frac{\ln (x)}{x^p}=\frac{\infty}{\infty}$$
Using the l'Hospital's rule it follows:
$$\lim_{x \to \infty}\frac{\frac{1}{x}}{px^{p-1}}=\lim_{x \to \infty}\frac{1}{pxx^{p-1}}=\lim_{x \to \infty}\frac{1}{px^{p}}=\frac{1}{p}\lim_{x \to \infty}\frac{1}{x^{p}}=\frac{1}{p} \cdot 0=0$$
