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Solve the fol...

Question

Solve the following equation:
$9^{| 3 x - 1 |} = 3^{8 x - 2}$

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Solution

$9^{∣ 3 x - 1 ∣} = 3^{8 x - 2}$
$3^{2 ∣ 3 x - 1 ∣} = 3^{8 x - 2}$
$∣ 3 x - 1 ∣= 4 x - 1$
$3 x - 1 = \pm (4 x - 1)$
$⟹ x = 0, \frac{2}{7}$

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