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.







 

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