If $3^{x} - 3^{x - 1} = 6$ , then $x^{x}$ is equal to

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Solution

The correct option is B
4

Finding the value:
Given $3^{x} - 3^{x - 1} = 6$
$\begin{array}{rcl} \Rightarrow & 3^{x} - \frac{3^{x}}{3} = 6 \\ \Rightarrow & 3^{x} (1 - ⅓) = 6 \\ \Rightarrow 3^{x} (⅔) & = & 6 \\ \Rightarrow & 3^{x} = 18 / 2 \\ \Rightarrow & = 9 \\ \Rightarrow & 3^{x} = 3^{2} \\ \Rightarrow & x = 2 \\ S o x^{x} & = & 2^{2} \\ \Rightarrow & = 4 \end{array}$
Hence option (B) is the answer.

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