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Question
`(2/3)^x (3/2)^(2x)=81/16 `then x =
Options
2
3
4
1
Solution
We have to find value of x provided `(2/3)^x (3/2)^(2x)=81/16 `
So,
`(2/3)^x (3/2)^(2x)=81/16 `
`(2/3)^x (3/2)^(2x)= 3^4/3^4`
`(2x)/(3x) (3^(2x))/(2^(2x)) = 3^4/2^4`
`3^(2x -x)/2^(2x-x) = 3^4/2^4`
`3^x/2^x = 3^4/2^4`
Equating exponents of power we get x = 4.
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