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8. （5 分） 设 $a=\log _{3} 2, b=\log _{5} 2, c=\log _{2} 3$, 则（ $）$

Gaokao · Math · previous-year question

  1. A.$a>c>b$
  2. B.$b>c>a$
  3. C.$c>a>b$correct
  4. D.$c>b>a$

Answer

C. $c>a>b$

Explanation

解: 由题意可知: $a=\log _{3} 2 \in(0,1), b=\log _{5} 2 \in(0,1), c=\log _{2} 3>1$, 所以 $a=\log _{3} 2, b=\log _{5} 2=\frac{\log _{3} 2}{\log _{3} 5}<\log _{3} 2$, 所以 $c>a>b$, 故选: C.

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