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AMO 2024 – Secondary 4 (Grade 10) Question 8

AMO · AMO 2024 – Secondary 4 (Grade 10)

Question 8

The source displays $x^{x^{x^{\cdot^{\cdot^{\cdot}}}}}=3$. Under its formal repeated-tail interpretation, what value of x follows? Clarification: treat the tail as 3 and solve $x^3=3$; this is a formal algebraic interpretation, not a claim that the usual sequence of finite power towers converges to 3.

Question illustration
  1. 3
  2. $1/3$
  3. $\sqrt[3]3$
  4. 1