if $3^{x} - 3^{x - 1} = 18$ , then $x^{x}$ is equal to

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 $27$
$3^{x} - 3^{x - 1} = 18$
$\Rightarrow 3^{x} - \frac{3^{x}}{3} = 18$
$\Rightarrow 3^{x} (\frac{2}{3}) = 18$
$3^{x - 1} .2 = 3^{2} .2$
$x - 1 = 2$
$∴ x = 3$
$x^{x} = 3^{3} = 27.$
Hence, the answer is $27.$

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$\frac{3 \times 27^{x + 1}}{3 \times 3^{3 x + 2}} + \frac{27 \times 3^{3 x}}{\frac{- 1}{3} \times 27^{x + 1}}$ is equal to ____.

If $3^{x - y}$ = 27and $3^{x + y}$ = 243, then x is equal to:

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