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MathNet 2020 — Math Olympiad Vault — Part 02 Question 120

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 02

Question 120

Let $a = 256$. Find the unique real number $x \gt a^{2}$ such that
$$
\log_{a} \log_{a} \log_{a} x = \log_{a^{2}} \log_{a^{2}} \log_{a^{2}} x
$$