[2024/05/13] Irrational powers

zkfcfbzr, 9 days ago (edited 9 days ago)

solutione^(i*π) = -1 Also, anything like a^(log(c) / log(a)), for positive rational c and irrational a, to generalize bean_jamming’s answer I also assert without proof that in the equation x^x = c, x is irrational for most rational values of c I did start trying out stuff with sqrt(2), thinking back to the tower power problems, but didn’t end up coming up with your solution while doing so ¯_(ツ)_/¯

been_jamming, 10 days ago

e^(log 2) = 2 is rational

siriusmart, 10 days ago

that is simply genius

(i suppose it didnt come to me when i think of “irrational”)

siriusmart, 10 days ago (edited 10 days ago)

this one got some table slams from my friends

Hint:

spoilerFind an example which satisfies the equation.

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Solution:

spoiler…siri.sh/…/2024-05-13_irrational-powers.htmlhttps://lemmy.world/pictrs/image/94a2af80-483f-4874-9864-ca1858e61546.png