Problem
Oops I Tripped On a Log
Author: munch
Define \{x_n\}, where n \in \mathbb{Z}^+ as the sequence such that x_i < x_j when i < j, and x_n satisfies the equation 0.8^{[x_n]} + \log_{0.8} \{x_n\} = x_n. If \alpha =\sum_{k=1}^{\infty} \{x_k\}, find \alpha^{\alpha}+\alpha^{\alpha+2}.
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