# 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 \(\log_{3}(x_{14}).\)