If $2^{x + 1} + 2^{x - 1} = 320$ , then the value if $x$ is

6

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8

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5

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7

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Solution

The correct option is B $7$
$2^{x + 1} + 2^{x - 1} = 320$
$\Rightarrow 2^{x} 2 + \frac{2^{x}}{2} = 320$
$\Rightarrow {4.2}^{x} + 2^{x} = 640$
$\Rightarrow 2^{x} (1 + 4) = 640$
$\Rightarrow 2^{x} = \frac{640}{5}$
$\Rightarrow 2^{x} = 2^{7}$
$\Rightarrow x = 7$

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