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Question
Determine `(8x)^x,`If `9^(x+2)=240+9^x`
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Solution
`9^(x+2)=240+9^x`
`rArr9^x xx 9^2=240+9^x`
`rArr9^x(9^2-1)=240`
`rArr9^x(81-1)=240`
`rArr9^x xx80=240`
`rArr9^x=240/80`
`rArr3^(2x)=3^1`
⇒ 2x = 1
`rArrx=1/2`
`therefore(8x)^x=(8xx1/2)^(1/2)=(4)^(1/2)=2`
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