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Product Law

If 2x+4-2x+...

Question

If $2^{x + 4} - 2^{x + 2} = 3$ , then $x$ is equal to

A

0

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B

2

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C

- 1

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D

- 2

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Solution

The correct option is D $- 2$
$2^{x + 4} - 2^{x + 2} = 3 \Rightarrow 2^{4} {.2}^{x} - 2^{2} {.2}^{x} = 3$
$\Rightarrow {16.2}^{x} - {4.2}^{x} = 3 \Rightarrow 2^{x} (16 - 4) = 3$
$2^{x} = \frac{3}{12} \Rightarrow 2^{x} = \frac{1}{4} \Rightarrow 2^{x} = 2^{- 2} \Rightarrow x = - 2$

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