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}(x_{n}) = 308 and 56 \leq \log_{3}\left ( \sum_{n=0}^{7}x_{n}\right ) \leq 57,

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

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.