If $3^{x} - 3^{x - 1} = 18$ , then the value of $x^{x}$ is

3

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8

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27

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216

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Solution

The correct option is C $27$
$3^{x} - 3^{x - 1} = 18 \Rightarrow 3^{x} - 3^{x} {.3}^{- 1} = 18$
$\Rightarrow 3^{x} (1 - \frac{1}{3}) = 18 \Rightarrow 3^{x} \times \frac{2}{3} = 18$
$\Rightarrow 3^{x} = \frac{18 \times 3}{2} = 27 = 3^{3} \Rightarrow x = 3$
$∴ x^{x} = 3^{3} = 27$

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