Let a real-valued sequence $\left\{x_{n}\right\}_{n \geq 1}$ be such that $$\lim_{n \rightarrow \infty} n x_{n} = 0$$ Find all possible real values of $t$ such that $\lim_{n \rightarrow \infty} x_{n}(\log n)^{t} = 0$.
Let a real-valued sequence $\left\{x_{n}\right\}_{n \geq 1}$ be such that
$$\lim_{n \rightarrow \infty} n x_{n} = 0$$
Find all possible real values of $t$ such that $\lim_{n \rightarrow \infty} x_{n}(\log n)^{t} = 0$.