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AMO 2021 – Junior College (Grades 11–12) Question 9

AMO · AMO 2021 – Junior College (Grades 11–12)

Question 9

Given $\log_a b+\log_b a=3$ and $a>b>1$, find $\log_a b-\log_b a$.

Question illustration
  1. $-\sqrt5$
  2. $-\sqrt3$
  3. $\frac12$
  4. $\sqrt3$
  5. $\sqrt5$