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

(第二十五届AIME2 2007 第12题)