Solving x^y=y^x
10-24-2018, 09:58 PM
Post: #7
 Albert Chan Senior Member Posts: 2,355 Joined: Jul 2018
RE: Solving x^y=y^x
(10-24-2018 07:37 PM)Dieter Wrote:  The WP34s, for example, handles this easily:

LN
RCL/ L
CHS
Wp
RCL/ L

Enter x, get y and vice versa.

Thanks, Dieter. I was curious how above get derived ...

Found a very close solution for infinite tetration c = x^c, or ln(c)/c = ln(x).
From the video (~ 7:00), using basic algebra, he got c = W(-ln(x)) / (-ln(x))

For x^y = y^x, ln(y)/y = ln(x)/x, so just substitute above: c=y, ln(x)=ln(x)/x
--> y = W(-ln(x)/x) / (-ln(x)/x)

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 Messages In This Thread Solving x^y=y^x - sasa - 10-24-2018, 06:06 PM RE: Solving x^y=y^x - Albert Chan - 10-24-2018, 07:21 PM RE: Solving x^y=y^x - Dieter - 10-24-2018, 07:37 PM RE: Solving x^y=y^x - John Keith - 10-24-2018, 08:23 PM RE: Solving x^y=y^x - CyberAngel - 10-28-2018, 08:22 PM RE: Solving x^y=y^x - sasa - 10-24-2018, 08:45 PM RE: Solving x^y=y^x - Albert Chan - 10-24-2018 09:58 PM RE: Solving x^y=y^x - ijabbott - 10-24-2018, 10:35 PM RE: Solving x^y=y^x - Erwin - 10-26-2018, 04:54 PM RE: Solving x^y=y^x - Albert Chan - 10-28-2018, 08:21 PM RE: Solving x^y=y^x - Erwin - 10-28-2018, 08:51 PM RE: Solving x^y=y^x - Tim Wessman - 10-29-2018, 03:14 AM RE: Solving x^y=y^x - sasa - 10-24-2018, 07:45 PM

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