1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Just wondering about x^y = y^x

  1. Nov 22, 2006 #1
    This wasnt set for homework just something i thought up so i hope this is the right place to post?

    Anyway when i put x^y = y^x (or also lnx/lny = x/y) in a graphing program i realised that there were two lines, y = x and another line that looked a bit like y = e^(e/x) but wasnt.


    So this kind of interested me... and i have two questions:

    can y^x = x^y be written as y = f(t) and x = g(t) and if so what are f(t) and g(t)?

    Is it possible to find the equation of just the line that looks like y = e^(e/x) ?


    I have thought about it a bit but have no idea how to go about solving either question. Any degree level maths will be beyond me (doing A level atm) so hopefully there is something simple that i have overlooked?
     
  2. jcsd
  3. Nov 22, 2006 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    How did you put xy= yx into a graphing program? Most graphing programs require that the function be put in the form y= f(x) which is the whole problem here.

    Solving yx= xy, or, equivalently, y= xy/x for y looks to me like it would involve the "Lambert W function", defined as the inverse to the function f(x)= xex.
     
  4. Nov 22, 2006 #3

    0rthodontist

    User Avatar
    Science Advisor

    There was an old thread about this. One thing you can do is graph in 3-d z = x^y - y^x
     
  5. Nov 22, 2006 #4
    I used a trial version of derive 6 and plugged x^y=y^x straight in. It only plotted for positive values and went a bit crazy at high values of x and y. I think it was fairly accurate though. I remember putting one of the values for the non x=y line into my calculator and it working.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Just wondering about x^y = y^x
  1. Y^x = x^y (Replies: 3)

  2. Y^x = x^y (Replies: 20)

  3. X^y=y^x REVISITED (Replies: 3)

  4. Solution of x^y=y^x (Replies: 2)

Loading...