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Question
Find the value of x, if `(4/7)^x (7/4)^(2x) = 343/64`.
Solution
Given: `(4/7)^x (7/4)^(2x) = 343/64`
`(4/7)^x (1/(4/7))^(2x) = 343/64`
`(4/7)^x (4/7)^(-2x) = 343/64`
`(4/7)^(x - 2x) = 343/64`
`(4/7)^-x = (7/4)^3`
`(4/7)^(-x) = (7/4)^-3`
Equating the exponents, we get
– x = – 3
⇒ x = 3
As a result, the value of x is 3.
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