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Base, Exponent and Power

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

Question

If $2^{x} - 2^{x - 1} = 4$ , then $x^{x}$ is equal to

A

7

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B

3

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C

27

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D

None of the above

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Solution

The correct option is B $27$
$2^{x} - 2^{x - 1} = 4$
$⟹ 2^{x - 1} (2 - 1) = 4$
$⟹ 2^{x - 1} = 2^{2}$
$⟹ x - 1 = 2$
$⟹ x = 2 + 1 = 3$
$∴ x^{x} = 3^{3} = 27$

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