MIND-BLOWING Math Olympiad Problem That ONLY 3% Can Solve!

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  • Опубликовано: 10 дек 2024

Комментарии • 3

  • @Ingb3rg
    @Ingb3rg 6 дней назад

    Niceeee.

  • @robinbernardinis
    @robinbernardinis 5 дней назад +2

    That's not the only solution, though.
    For x = 1, LHS is bigger.
    For x = 2, RHS is bigger.
    Both sides are continuous, so there must be another solution between 1 and 2, but very close to 1. I don't know how to solve it, but WolframAlpha says it's about 1.0025851, and my calculator agrees.
    As far as how to find the integer solution, the way I did it is to take the base 5 log, you get
    x = 625 log_5(x)
    Let y = log_5(x)
    5^y = 5^4 y
    5^(y-4) = y
    If y is an integer, y must be a power of 5. Try y=5, you get
    5^(5-4) = 5, which is true
    x = 5^y = 5^5 = 3125