If 3^x - 3^ x - 1 = 6, then x^x is equal to - Vidyadip

Question

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

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Answer

b
(b) We have ${3^x} - {3^{x - 1}} = 6$

==> ${3^x} - \frac{{{3^x}}}{3} = 6$

Let ${3^x} = t$, then given equation can be written as

$t - \frac{t}{3} = 6$ ==> $3t - t = 18$ ==> $2t = 18$ ==> $t = 9$

$\therefore$ ${3^x} = {3^2}$ ==> $x = 2$.

Hence, ${x^x} = {2^2} = 4$.

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