2007 AIME II Problem 12

The increasing geometric sequence x_{0}, x_{1}, x_{2}, \ldots consists entirely of integral powers of 3.
Given that $$ \sum_{n=0}^{7} \log {3}\left(x{n}\right)=308 \quad \text { and } \quad 56 \leq \log {3}\left(\sum{n=0}^{7} x_{n}\right) \leq 57
$$ find \log _{3}\left(x_{14}\right).