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

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