SOLUTION: Solve for x: (x^2-7x+7)^(x^2-9x+20)=1

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Question 1096954: Solve for x: (x^2-7x+7)^(x^2-9x+20)=1
Found 3 solutions by Fombitz, MathTherapy, ikleyn:
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website!
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Answer by MathTherapy(10555)   (Show Source):
You can put this solution on YOUR website!
Solve for x: (x^2-7x+7)^(x^2-9x+20)=1

Except 0, any EXPRESSION/VALUE that's raised to the 0 power = 1

Therefore,
(x - 5)(x - 4) = 0 =====>

Answer by ikleyn(52835)   (Show Source):
You can put this solution on YOUR website!
.

Also (as an addition to the @MathTutor's solution) if the base x^2 - 7x + 7 = 1, then any degree of the base is 1. x^2 - 7x + 7 = 1 ====> x^2 -7x + 6 = 0 ====> (x-6)*(x-1) = 0 ====> the roots are x= 6 and x= 1.

So, add these values x= 6 and x= 1 to the list of solutions.