If 9 $^{x + 2}$ = 240 + 9 $^{x}$ then the value of x is:

0.1

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0.2

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0.3

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0.4

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0.5

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Solution

The correct option is D $0.5$
$9^{x + 2} = 240 + 9^{x}$
add 3 on both sides
$\Rightarrow 9^{x + 2} + 3 = 243 + 9^{x}$
$\Rightarrow 3^{2 x + 4} + 3 = 3^{5} + 3^{2 x}$
On rearranging
$3^{2 x + 4} - 3^{2 x} = 3^{5} - 3$
$3^{2 x} (3^{4} - 1) = 3 (3^{4} - 1)$
$3^{2 x} = 3$
$\Rightarrow 2 x = 1$
$\Rightarrow x = 0.5$

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Find the following pair of linear equations by the substituting method:-

(a) 3x-y=3

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