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HMMT 二月 2009 · 冲刺赛 · 第 8 题

HMMT February 2009 — Guts Round — Problem 8

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 6 ] Which is greater, log (2009) or log (2010)?
    2008 2009
解析

英文解析

  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 isx 2
    x ( x +1) ln xdecreasing. Thus log (2009) is greater.
    2008