Solve 2^2x -12*2^x + 32 = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to solve: 2^2x -12*2^x + 32 = 0

2^2x -12*2^x + 32 = 0

Let 2^x = y

=> y^2 - 12y + 32 = 0

=> y^2 - 8x - 4x + 32 = 0

=> y(y - 8) - 4(y - 8) = 0

=> (y - 4)(y - 8) = 0

=> y = 4 and y = 8

As 2^x = y

2^x = 4

=> x = 2

and 2^x = 8

=> x = 3

The solution of the given equation is x = 2 and x = 3

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