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Determine `(8x)^X,`If `9^(X+2)=240+9^X` - Mathematics

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ConceptLaws of Exponents for Real Numbers

Question

Determine `(8x)^x,`If `9^(x+2)=240+9^x`

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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Solution Determine `(8x)^X,`If `9^(X+2)=240+9^X` Concept: Laws of Exponents for Real Numbers.
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