Question
If `(9/4)^x.(8/27)^(x - 1) = 2/3` , then the value of `x` is :
Answer: Option D
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`(9/4)^x.(8/27)^(x - 1) = 2/3` `hArr` ` 9^x/4^x xx 8^(x - 1)/(27)^(x - 1) = 2/3`
`hArr (3^2)^x/(2^2)^x xx((2^3)^(x - 1))/((3^3)^(x - 1)) = 2/3 hArr (3^(2x) xx 2^(3(x- 1)))/(2^(2x) xx 3^(3(x - 1))) = 2/3`
`hArr (2^((3x - 3 -2x)))/(3^((3x - 3 - 2x))) = 2/3 hArr (2^((x-3)))/(3^((x- 3))) = 2/3 hArr (2/3)^(x -3)`
=`(2/3)^1 hArr x - 3 = 1 hArr x = 4.`
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