If $2^{x + 1} = 8^{x - 3}$ , then $x$ is equal to:

2

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3

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4

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5

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6

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Solution

The correct option is C $5$
Given, $2^{x + 1} = 8^{x - 3}$
Since $8 = 2^{3}$ , therefore, $8^{x - 3}$ may be written as ${(2)}^{3 (x - 3)}$ that is $2^{3 x - 9}$
Now, it is given that $2^{x + 1} = 8^{x - 3}$ equating the powers of $2^{x + 1}$ and $2^{3 x - 9}$ to find the value of $x$ :
$\Rightarrow x + 1 = 3 x - 9$
$\Rightarrow 3 x - x = 9 + 1$
$\Rightarrow 2 x = 10$
$\Rightarrow x = 5$

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