Solve : $9 x = 2 = 720 + 9^{x}$

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Solution

$9^{x + 2} = 720 + 9^{x}$
$\Rightarrow 9^{x + 2} - 9^{x} = 720$
$\Rightarrow 9^{x} (9^{2} - 1) = 720$
$\Rightarrow 9^{x} (81 - 1) = 720$
$\Rightarrow 9^{x} (80) = 720$
$\Rightarrow 9^{x} = 9$
$\Rightarrow 9^{x} = 9^{1}$
$\Rightarrow x = 1$

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