If $9^{2 x - 1} - 81^{x - 1} = 1944$ , then x is

3

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\frac{9}{4}

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\frac{4}{9}

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\frac{1}{3}

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Solution

The correct option is B $\frac{9}{4}$
$9^{(2 x - 1)} - 81^{(x - 1)} = 1944 9^{(2 x - 1)} - 9^{(2 x - 2)} = 1944 9^{2 x - 2} \times 8 = 1944, 3^{(4 x - 4)} = 3^{5} 4 x - 4 = 5 x = \frac{9}{4}$

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