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Solve , log((2x -3)) (x^(2) - 5x + 7) =...

Solve , ` log_((2x -3)) (x^(2) - 5x + 7) = 2 `

Text Solution

Verified by Experts

The equivalent form of the given equation is ` x^(2) - 5x + 7 = (2x - 3)^(2) " where" x gt (3)/(2)` and
` 2x - 3 ne 1, 2x ne 4, x ne 2 `
` rArr x^(2) - 5x + 7 = 4x^(2) - 12 + 9 `
`rArr 3x^(2) - 6x - x + 2 = 0`
` rArr 3x (x - 2) - 1 (x - 2) = 0 `
`rArr (3x - 1) - (x-2) = 0 `
`rArr x = (1)/(3) , 2`
Since ` s gt (3)/(2) "and" x ne 2 rArr` the given equation does not have any solution .
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