A recursive sequence is defined as $a_0=\pi$ and $a_n=\log_{a_{n-1}}{27}.$

Given that $\displaystyle\lim_{n\to\infty}{a_n}$ exists, what is $\displaystyle\lim_{n\to\infty}{a_n}?$

**Bonus:** For what values of $a_0$ does $\displaystyle\lim_{n\to\infty}{a_n}$ exist?

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