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HMMT 二月 2014 · 代数 · 第 3 题

HMMT February 2014 — Algebra — Problem 3

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Let 1 3 3 3 3 A = (log (3)) (log (6)) (log (12)) + (log (24)) . 2 2 2 2 6 A Compute 2 . 2
解析
  1. Let ( ) 1 3 3 3 3 A = (log (3)) − (log (6)) − (log (12)) + (log (24)) . 2 2 2 2 6 A Compute 2 . 1 a 3 3 3 3 Answer: 72 Let a = log (3), so 2 = 3 and A = [ a − ( a + 1) − ( a + 2) + ( a + 3) ]. But 2 6 1 1 3 3 2 2 2 ( x + 1) − x = 3 x + 3 x + 1, so A = [3( a + 2) + 3( a + 2) − 3 a − 3 a ] = [4 a + 4 + 2] = 2 a + 3. Thus 6 2 A a 2 3 2 = (2 ) (2 ) = 9 · 8 = 72. 2