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Question

If $2^{x} + 2^{x + 2} = 40$ , then the value of $x$ is
$1$
$2$
$4$
$3$

A

1

B

2

C

3

D

4

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Solution

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Given, $2^{x} + 2^{x + 2} = 40 \Rightarrow 2^{x} + 2^{2} 2^{x} = 40 \Rightarrow 2^{x} + (4) 2^{x} = 40 \Rightarrow (5) 2^{x} = 40 \Rightarrow 2^{x} = 8 \Rightarrow 2^{x} = 2^{3}$
So, $x = 3$

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