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SMO 2015 Senior Round 1 Question 9

SMO · SMO 2015 Senior Round 1

Question 9

How many prime numbers $p$ satisfy the inequality $$\left|2+\log_{3/p}(3p^2)\right|\gt \frac32?$$
  1. 6
  2. 7
  3. 8
  4. 9
  5. 10