[OT] x**y == y**x

Marko Rauhamaa marko at pacujo.net
Fri Jan 9 22:41:15 CET 2015


Peter Pearson <pkpearson at nowhere.invalid>:

> If you've never looked at the set of reals (x,y) satisfying x**y ==
> y**x, it's worth a visit.

Thanks, it was. The graph's something like this:



  |         : *
  |         : *
  |         : *
  |         :  *
6 +         :  *                                              *
  |         :  *                                            **
  |         :   *                                         **
  |         :   *                                       **
  |         :    *                                    **
5 +         :    *                                  **
  |         :     *                               **
  |         :      *                            **
  |         :       *                         **
  |         :        *                      **
4 +         :         *                   **
  |         :          *                **
  |         :           *             **
  |         :            *          **
  |         :             *       **
3 +         :              *    **
  |         :               * **
  |         :               ***
  |         :             **   *****
  |         :           **          ***
2 +         :         **               *********
  |         :       **                          **
  |         :     **                              *******
  |         :   **                                       ******
  |         : **
1 +.........**.................................................
  |       **:
  |     **  :
  |   **    :
  | **      :
  +*--------+---------+---------+---------+---------+---------+
            1         2         3         4         5         6

where the line and the arc intersect at (e, e).

Where can I read more on the topic?


Marko



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