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Q.

Find the value of $x$ under the given condition, $9^{x + 2} = 240 + 9^{x}$ is

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a

0.1

b

0.2

c

0.3

d

0.5

answer is D.

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Detailed Solution

Given condition:

9^{x + 2} = 240 + 9^{x}

9^{x} . 9^{2} - 9^{x} = 240

9^{x} (81 - 1) = 240

9^{x} (80) = 240

9^{x} = \frac{240}{80}

9^{x} = 3

{(3^{2})}^{x} = 3^{1}

3^{2 x} = 3^{1}

2x = 1

x = \frac{1}{2} = 0.5

Hence, option (4) is correct.

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