Find n, $6^{2 n - 1} \div 6^{2} = 6^{3}$

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Solution

Given $6^{2 n - 1} \div 6^{2} = 6^{3}$
$\frac{6^{2 n - 1}}{6^{2}} = 6^{3}$
$6^{2 n - 1 - 2} = 6^{3}$
$⟹ 2 n - 3 = 3 ⟹ 2 n = 6 ⟹ n = 3$

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