Solve for x: 4^x - 2^(x + 3) = 9

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation `4^x - 2^(x + 3) = 9` has to be solved for x.

`4^x - 2^(x + 3) = 9`

=> `2^(2x) - 2^x*8 = 9`

let `2^x = y`

=> `y^2 - 8y - 9 = 0`

=> `y^2 - 9y + y - 9 = 0`

=> `y(y - 9) + 1(y - 9) = 0`

=> `(y + 1)(y - 9) = 0`

=> y = -1 and y = 9

`y = 2^x` cannot be negative, the root y = -1 can be eliminated. This gives `2^x = 9`

=> `x = log 9/log 2`

The solution of the equation `4^x - 2^(x + 3) = 9` is `x = log 9/log 2`

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