If $9^{x + 2} = 240 + 9^{x}$ , then $x =$

0.5

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0.2

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0.4

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0.6

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Solution

The correct option is A $0.5$
$9^{x + 2} = 240 + 9^{x}$
$\Rightarrow$ $9^{x} .81 = 240 + 9^{x}$
$\Rightarrow$ ${80.9}^{x} = 240$
$\Rightarrow$ $9^{x} = 3$
$\Rightarrow$ $3^{2 x} = 3$
$\Rightarrow$ $2 x = 1$
$\Rightarrow$ $x = 0.5$

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