Solving x^y=y^x
10-24-2018, 07:37 PM (This post was last modified: 10-24-2018 07:38 PM by Dieter.)
Post: #3
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: Solving x^y=y^x
(10-24-2018 06:06 PM)sasa Wrote:  This guy have quite interesting samples to play with...
Is it possible to solve this one on Prime?

I didn't watch the video, but this equation can be directly solved by means of the Lambert W function.
The WP34s, for example, handles this easily:

LN
RCL/ L
CHS
Wp
RCL/ L

Enter x, get y and vice versa.

Replace Wp with Wm (the other branch of Lambert's W function) and get the second solution. For x=e both solutions are equal (x=y=e)

X=2 => Y=2
X=3 => Y=2,47805268...
X=4 => Y=2

So, does the Prime feature the W function?

Dieter
 « Next Oldest | Next Newest »

 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

User(s) browsing this thread: 1 Guest(s)