# Limit of a Log Sequence

Being the sequence: $$\left\{X_n\right\}=\log_{a}{(n)}\ ; a>1$$

I'm having difficulty figuring out what to do to prove in this sequence, the existence of this limit,

$$\lim_{n \to \infty} \log_{a}{(n)}\ ; a>1$$

I've been investigating, but just cannot seem to figure it out, any help/hint would be appreciated, many thanks.

• Hint: What if $n > a^m$? – Antonio Vargas Nov 21 '17 at 0:54