Skip to content / Đến nội dung
ThichHocToan.com

SMO 2011 Open Round 1 Question 13

SMO · SMO 2011 Open Round 1

Question 13

Let $x[n]$ denote the right-associated power tower $x^{x^{\cdot^{\cdot^x}}}$ with $n$ copies of $x$. What is the minimum $n$ such that $9[9]\lt 3[n]$? For example, $3[2]=3^3=27$ and $2[3]=2^{2^2}=16$.