$D e t e r m i n e (8 x)^{x}, i f 9^{x + 2} = 240 + 9^{x} .$

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Solution

$9^{x + 2} = 240 + 9^{x} 9^{x} \times 9^{2} = 240 + 9^{x} \Rightarrow 9^{x} \times 81 = 9^{x} + 240 81 \times 9^{x} - 9^{x} = 240 \Rightarrow 80 \times 9^{x} = 240 \Rightarrow 9^{x} = \frac{240}{80} = 3 \Rightarrow 3^{2 x} = 3^{1} ∴ 2 x = 1 \Rightarrow x = \frac{1}{2} N o w, (8 x)^{x} = {(8 \times \frac{1}{2})}^{\frac{1}{2}} = 4^{\frac{1}{2}} = (2^{2})^{\frac{1}{2}} = 2^{1} = 2$

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