I have to prove the following:
Let $n \in \mathbb{N}$. Proove:
$e^{\sqrt{\log x}}=O(x^n) .$
I just know the definition of $O$:
$f(x), g(x)$ are real functions. $f(x)=O(g(x))$ means, that for large $x$, $|f(x)| \leq C \cdot g(x)$ holds.
I'm a little bit confused, because I thought $O$ is part of the analysis and not number theory (in analysis I used it for Taylor series). Anyone can give me a hint where to start (or show an other example?). Best regards.