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SMO 2011 Senior Round 1 Question 7

SMO · SMO 2011 Senior Round 1

Question 7

Let $x=\frac1{\log_{1/3}(1/2)}+\frac1{\log_{1/5}(1/4)}+\frac1{\log_{1/7}(1/8)}$. Which statement is true?
  1. $1.5\lt x\lt2$
  2. $2\lt x\lt2.5$
  3. $2.5\lt x\lt3$
  4. $3\lt x\lt3.5$
  5. $3.5\lt x\lt4$