If $3^{x} + 3^{x + 1} = 108$ , find the value of $(9 x)^{1 / x}$ .

3

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9

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15

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27

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Solution

The correct option is A $3$
$3^{x} + 3^{x + 1} = 108$

$3^{x} + 3^{x} {.3}^{1} = 108$

${4.3}^{x} = 108$

$3^{x} = \frac{108}{4} = 27$

$3^{x} = 3^{3}$

$\Rightarrow x = 3$

Now,
${(9 x)}^{\frac{1}{x}}$ $= {(9 \times 3)}^{\frac{1}{3}}$

$= {(3^{3})}^{\frac{1}{3}}$

$= {(3)}^{\frac{1}{3} \times 3}$

$= 3$

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