this post was submitted on 06 May 2024
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Daily Maths Challenges

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  • Solve x for x^x*x^x^ = 2
  • Note that the Lambert W function W(x) is the inverse of f(x) = xe^x^
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[–] [email protected] 3 points 4 months ago* (last edited 4 months ago) (1 children)

This is a genuinely fun one

hint 1 (don't peek unless you really need it)

spoilertry solving a simpler version of the problem


hint 2 (supplementary to hint 1)

spoilerthe simpler version is x^x^=2


hint 3 (unrelated to 1 and 2)

spoilerx^x*x^x^=(x^x^)^(x^x^)


hint 4 (its basically the answer)

spoilerx^x^=e^(ln x)(e^(ln x))


Solution: https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-05_fake-power-tower.html

spoiler