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Solve the equation 12*(4^x) - 12*2^x + 3 = 0

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lxsptter | Student, Undergraduate | (Level 2) Valedictorian

Posted April 27, 2013 at 5:02 PM via web

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Solve the equation 12*(4^x) - 12*2^x + 3 = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 27, 2013 at 5:06 PM (Answer #1)

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The equation `12*(4^x) - 12*2^x + 3 = 0` has to be solved.

`12*(4^x) - 12*2^x + 3 = 0`

=> `4*(4^x) - 4*2^x + 1 = 0`

Let `2^x = y => 4^x = (2^2)^x = 2^(2x) = y^2`

=> `4y^2 - 4y + 1 = 0`

=> `(2y - 1) = 0`

=> `y = 1/2`

=> `2^x = 1/2`

=> `x = -1`

The solution of the equation is x = -1.

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