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  4. The roots of the equation 22x - 10. 2x + 16 = 0 are

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Q. The roots of the equation
$2^{2x} - 10. 2^x + 16 = 0$ are

Complex Numbers and Quadratic Equations

Solution:

$2^{2x} - 10.2^x + 16 = 0$
$\Rightarrow $ $(2^x - 8) (2^x - 2) = 0$
$\Rightarrow \, 2^x = 8, 2^x = 2 $
$\Rightarrow \, 2^x = 2^3, 2^x = 2^1$
$ \Rightarrow \, x = 3, x = 1 $