If $3^{x + 3} = 9^{x + 1},$ then

x = 2

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x = 1

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x = 3

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x = 4

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Solution

The correct option is B $x = 1$
We have,
$3^{x + 3} = 9^{x + 1}$
$\Rightarrow 3^{x + 3} = (3^{2})^{x + 1}$
$\Rightarrow 3^{x + 3} = 3^{2 x + 2}$
Since the bases are same, so compare the powers
i.e., $x + 3 = 2 x + 2$
$\Rightarrow 2 x - x = 3 - 2$
$\Rightarrow x = 1$
So, $B$ is the correct option.

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