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Factorization Method Form to Remove Indeterminate Form

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

Question

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

A

2

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B

- 1

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C

– 2

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D

1

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Solution

The correct option is C
– 2

$\begin{matrix} 2^{x + 4} - 2^{x + 2} = 3 \Rightarrow 2^{x + 4} (2^{2} - 1) = 3 \Rightarrow 2^{x + 2} . 3 = 3 \Rightarrow 2^{x + 2} = 1 = 2^{0} \Rightarrow x + 2 = 0 \Rightarrow x = - 2. \end{matrix}$

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