Lovely Logarithm!

Algebra Level 5

$\begin{eqnarray} &\displaystyle\sum_{n=0}^{7}\log_{3}(x_{n}) &= 308 \\ 56 \leq & \log_{3}\left ( \sum_{n=0}^{7}x_{n}\right )& \leq 57 \\ \end{eqnarray}$

The increasing geometric sequence $$x_{0},x_{1},x_{2},\ldots$$ consists entirely of integral powers of 3. If they satisfy the two conditions above, find $$\log_{3}(x_{14}).$$

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