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HMMT 二月 2009 · 冲刺赛 · 第 8 题

HMMT February 2009 — Guts Round — Problem 8

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 6 ] Which is greater, log (2009) or log (2010)? 2008 2009
解析
  1. [ 6 ] Which is greater, log (2009) or log (2010)? 2008 2009 Answer: log 2009 . 2008 x ln x − ( x +1) ln( x +1) ′ Solution: Let f ( x ) = log ( x + 1). Then f ( x ) = < 0 for any x > 1, so f is 2 x x ( x +1) ln x decreasing. Thus log (2009) is greater. 2008