{"id":3440,"date":"2024-01-27T12:33:15","date_gmt":"2024-01-27T17:33:15","guid":{"rendered":"https:\/\/josmfs.net\/?p=3440"},"modified":"2024-04-05T10:20:10","modified_gmt":"2024-04-05T14:20:10","slug":"special-log-sum","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2024\/01\/27\/special-log-sum\/","title":{"rendered":"Special Log Sum"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3438\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/01\/Special-Log-Sum-Fig2.jpg\" alt=\"\" width=\"200\" height=\"241\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/01\/Special-Log-Sum-Fig2.jpg 400w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/01\/Special-Log-Sum-Fig2-248x300.jpg 248w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>Here is a fairly computationally challenging 1994 AIME problem .<\/p>\n<p>\u201cFind the positive integer <em>n<\/em> for which<\/p>\n<p style=\"text-align: center;\">\u230alog<sub>2<\/sub> 1\u230b + \u230alog<sub>2<\/sub> 2\u230b + \u230alog<sub>2<\/sub> 3\u230b + \u2026 + \u230alog<sub>2<\/sub> <em>n<\/em>\u230b = 1994.<\/p>\n<p>where for real <em>x<\/em>, \u230a<em>x<\/em>\u230b is the greatest integer \u2264\u00a0 <em>x<\/em>.\u201d<\/p>\n<p>There is some fussy consideration of indices.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Special-Log-Sum-Answer.jpg\">Answer<\/a><\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/01\/Special-Log-Sum-240111.pdf\">Special Log Sum<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is a fairly computationally challenging 1994 AIME problem . \u201cFind the positive integer n for which \u230alog2 1\u230b + \u230alog2 2\u230b + \u230alog2 3\u230b + \u2026 + \u230alog2 n\u230b = 1994. where for real x, \u230ax\u230b is the greatest integer \u2264\u00a0 x.\u201d There is some fussy consideration of indices. Answer See the Special Log [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[238,230],"class_list":["post-3440","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-aime","tag-sequences-and-series"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3440","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=3440"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3440\/revisions"}],"predecessor-version":[{"id":3501,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3440\/revisions\/3501"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3440"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3440"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3440"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}