Solving A Cool Exponential Equation

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[nasrullahhusnan]

x^x=2^(1-x²)
Note that x >0, as if x is negative, LHS will be negative but RHS is positive.
Take log: xln(x)=(1-x²)ln(2)
If x<1, LHS<0 while RHS>0
If x>1, LHS>0 while RHS<0
If x=1, LHS=1 and RHS=2^(1-1²)=1
Therefore x=1 is the only solution

[doctorb]

I was going to mention the hole at (0, 1) just as you did. I've always like the function y = x*x.

[benjaminvatovez]

Let x a positive real number:
1) if 0<x<1 then x ln(x) < 0 and (1-x²) ln(2) > 0 thus no solution
2) x=1 is a solution
3) if x > 1 then x ln(x) > 0 and (1-x²) ln(2) < 0 thus no solution
Conclusion: x=1 is the only solution.

[freddyalvaradamaranon]

Muy interesante ejercicio de ecuaciones exponenciales, muchas gracias por compartir el procedimiento 😊❤😊.

[claudelebourlegat]

since several months you propose exercises with obvious solutions. i didn't like it anymore