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What is the solution of the equation 2^(4x) - 6*2^(2x) + 2 = 0

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xataexa | Student, Kindergarten | Salutatorian

Posted June 21, 2013 at 5:02 PM via web

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What is the solution of the equation 2^(4x) - 6*2^(2x) + 2 = 0

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justaguide | College Teacher | (Level 1) Adjunct Educator

Posted June 21, 2013 at 5:08 PM (Answer #1)

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The solution of `2^(4x) - 6*2^(2x) + 2 = 0` has to be determined.

Let `2^(2x) = y` , the given equation is now:

y^2 - 6y + 2 = 0

The roots of this quadratic equation are `3-sqrt 7` and `3 + sqrt 7`

As `y = 2^(2x)`

`2^(2x) = 3 - sqrt 7`

=> `x = (log(3 - sqrt 7))/(2*log 2)`

and `2^(2x) = 3 + sqrt 7`

=> `x = (log(3 + sqrt 7))/(2*log 2)`

The solution of the given equation is `(log(3 +- sqrt 7))/(2*log 2)`

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