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)