3 ms·
I asked the same question a while ago, https://math.stackexchange.com/questions/613946/xx-y-given-y-solve-for-x-analytically https://math.stackexchange.com/ques
by anon1253 7y ago
I asked the same question a while ago, https://math.stackexchange.com/questions/613946/xx-y-given-y-solve-for-x-analytically https://math.stackexchange.com/questions/613946/xx-y-given-y...
Interesting analysis of the problem :-) it has been bugging me since high school!
Might be worth linking to the Lambert W function https://en.wikipedia.org/wiki/Lambert_W_function https://en.wikipedia.org/wiki/Lambert_W_function
This was the best comment I'd reckon:
> As you probably saw, the solution of x^x = y is x = Log(y) / W[Log(y)]. Now you take us in a highly philosophical debate. What is the limit of elementary functions ? Thanks for this question. Cheers. – Claude Leibovici
- edflsafoiewq 7y agoThat comment references the worked examples that used to be on the Lambert W wiki page, including this exact problem, x^x=y. Here's the last version before it was deleted if anyone wants to see it: https://en.wikipedia.org/w/index.php?title=Lambert_W_function&oldid=910867451#Example_2 https://en.wikipedia.org/w/index.php?title=Lambert_W_functio...
- pickdenis 7y agoI'm glad to see that this problem bugged other high schoolers. I spent a lot of time learning about the lambert W function and real analysis in general due to this problem in high school.