Limit of log(x)/x^a=0

Theorem

The following formula holds for $a \in \mathbb{C}$ with $\mathrm{Re}(a)>0$: $$\displaystyle\lim_{x \rightarrow \infty} \dfrac{\log(x)}{x^a} = 0,$$ where $\log$ denotes the logarithm.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.30$