{"status": "success", "data": {"description_md": "**Author:** munch\n\nDefine $\\{x_n\\}$, 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 $\\alpha =\\sum\\limits_{k=1}^{\\infty} \\{x_k\\}$, find $\\alpha^{\\alpha}+\\alpha^{\\alpha+2}$. ", "description_html": "<p><strong>Author:</strong> munch</p>&#10;<p>Define <span class=\"katex--inline\">\\{x_n\\}</span>, where <span class=\"katex--inline\">n \\in \\mathbb{Z}^+</span> as the sequence such that <span class=\"katex--inline\">x_i &lt; x_j</span> when <span class=\"katex--inline\">i &lt; j</span>, and <span class=\"katex--inline\">x_n</span> satisfies the equation <span class=\"katex--inline\">0.8^{[x_n]} + \\log_{0.8} \\{x_n\\} = x_n</span>. If <span class=\"katex--inline\">\\alpha =\\sum\\limits_{k=1}^{\\infty} \\{x_k\\}</span>, find <span class=\"katex--inline\">\\alpha^{\\alpha}+\\alpha^{\\alpha+2}</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 7, "problem_name": "Oops I Tripped On a Log ", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}