The value of $x$ satisfying the equation $6^{2 x + 4} = (3^{3 x}) (2^{x + 8})$ is

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Solution

$6^{2 x + 4} = 3^{3 x} \cdot 2^{x + 8}$
$\Rightarrow 6^{4} \cdot 3^{2 x} \cdot 2^{2 x} = 3^{3 x} \cdot 2^{x + 8}$
$\Rightarrow 6^{4} = 3^{x} \cdot 2^{8 - x}$
$\Rightarrow 3^{4} \cdot 2^{4} = 3^{x} \cdot 2^{8 - x}$
$∴ x = 4$ .

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