If $9^{x - 1} = 3^{2 x - 1} - 486$ ,then the value of x is:

\frac{7}{2}

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Solution

The correct option is B $\frac{7}{2}$
$9^{x - 1} = 3^{2 x - 1} - 486$
$3^{2 x - 1} = 9^{x - 1} t 486$
$\frac{3^{2 x}}{3} = 3^{2 x - 2} + 486$
$3^{2 x} = \frac{3 (3^{2 x})}{3^{z}} t (486) 3$
$3^{2 q} = 3^{2 x - 1} + 1458$
$2177 = 729 + 1458$
$3^{7} = 3^{6} + 1458$
$2 x = 7$
$x = \frac{7}{2}$

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If $486 * 7$ is divisible by $9,$ then the least value of $*$ is
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