If $3^{x + 2} - 3^{x} = 6^{3} (3^{8})$ , find the value of $x$ ___

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Solution

$3^{x + 2} - 3^{x} = 6^{3} (3^{8})$
$\Rightarrow 3^{x} (3^{2}) - 3^{x} = 6^{3} (3^{8})$
$\Rightarrow 3^{x} (9 - 1) = 6^{3} (3^{8})$
$\Rightarrow 3^{x} = \frac{6^{3}}{8} (3^{8})$
$\Rightarrow 3^{x} = \frac{256}{8} (3^{8})$
$\Rightarrow 3^{x} = 3^{3} 3^{8}$
$\Rightarrow 3^{x} = 3^{11}$
$∴ x = 1$

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