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solve the equation 4^x^2-80=16^x

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2 Answers

4^x^2-80=16^x  submitted.  I am going to assume
4x2-80=16x or      4x2-16x-80=0 is what is intended
divide by 4 to get x2-4x-20=0 whose solution by formula is
(4±√(16+80))/2=2±2√6
As for the form submitted, graph it.  It's tall skinny slightly lopsided "v"
Just to clarify, is this the problem you are trying to answer?
 
4x^2 - 80 = 16x
 
As in, 4 raised to the power x2 minus 80 equals 16 raised to the power x?
 
OR
 
Do you mean:
 
4x^2 - 80 = 16x
 
As in, 4 raised to the power x2 -80 equals 16 raised to the power x?
 
-Bailey S.

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This way, there is solution:
 
      4(X^2 -80 ) = 42x,  
       Then ,   X2 - 80 = 2X
                     
                   X2 - 2X - 80 =
 
                    ( X- 10) ( X + 8) = 0
 
                       X- 10 = 0    X = 10
                       X + 8 = 0    X= -8
     
    
 For:
          
    (4X )2 - 80 = 42x
 
    There is no solution:   

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