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Complex Numbers

If 2x-2x-1=...

Question

If $2^{x} - 2^{x - 1} = 4$ , then what is the value of $2^{x} + 2^{x - 1}$ ?

A

8

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B

12

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C

10

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D

16

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Solution

The correct option is A $12$
$2^{x} - 2^{x - 1} = 4$
$\Rightarrow 2^{x} - \frac{2^{x}}{2} = 4$
$\Rightarrow 2^{x} (1 - \frac{1}{2}) = 4$
$\Rightarrow 2^{x} \times \frac{1}{2} = 4$
$\Rightarrow 2^{x} = 8$
$\Rightarrow 2^{x} = 2^{3}$
Base are same
$\Rightarrow x = 3$
$∴ 2^{x} + 2^{x - 1} = 2^{3} + 2^{2}$ $= 8 + 4 = 12$

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