log

Joe Riel — Sun, 26 Feb 2012 09:24:45 Z

You should be able to solve that manually. When does y^x = 1?

Complex solutions

Markiyan Hirnyk — Sun, 26 Feb 2012 17:36:51 Z

There is an infinite set of complex solutions. For example,
> sol := solve((x-2)^(25-x^2) = 1, AllSolutions);

> A := op(2, allvalues(sol));

                        5.104852539 + 0.5252917772 I
> eval((x-2)^(25-x^2), x = A);


                      1.000000004 + 1.353864774 10 ^(-10)* I

The others can be found as (see http://en.wikipedia.org/wiki/Complex_logarithm )
> solve(exp(ln(x-2)*(25-x^2)) = 1, AllSolutions);


     exp(RootOf(_Z (exp(_Z))^2 + 4 _Z exp(_Z) - 21 _Z + 2 I Pi _Z38)) + 2

by

> fsolve(exp(ln(x-2)*(25-x^2)) = 1, x, complex);

                        5.104852539 + 0.5252917772 I
> fsolve(exp(ln(x-2)*(25-x^2)) = 1, x, avoid = {x = 5.104852539+.5252917772*I}, complex);

                        -3.026344426 - 2.007636723 I

and so on.
PS. Or if you prefer the original form of the equation,

> fsolve((x-2)^(25-x^2) = 1, x, complex);

5.104852539 + 0.5252917772 I

25-x^2 = 0 x = 5

marram — Sun, 26 Feb 2012 12:32:36 Z

25-x^2 = 0

x = 5

x=-5, x=3 and x=1 as well

Jarekkk — Sun, 26 Feb 2012 13:44:42 Z

@marram x can be equal to -5 or to 3 or to 1 as well.

MaplePrimes - answers and comments on Question, Solve the equation Please help me ! (IMO 2011-2012)

log

Complex solutions

25-x^2 = 0 x = 5

x=-5, x=3 and x=1 as well