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The number of solutions of the equation ...

The number of solutions of the equation `log_(x+1)(x-0.5)=log_(x-0.5)(x+1)` is

A

two real solutions

B

no prime solution

C

one integral solution

D

no irrational solution

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
`(log_(2)(x-0.5))/(log_(2)(x+1)) = (log_(2)(x+1))/(log_(2)(x-0.5))`
` or [log_(2)(x+1)]^(2)=[log_(2)(x-0.5)]^(2)`
` :. log_(2)(x+1)=pmlog_(2)(x-0.5)`
If ` log_(2)(x+1)=log_(2)(x-0.5)`.Then,
` x + 1 = x - 0.5 `, hence no solution
If ` log_(2)(x+1)= log(x-0.5)^(-1)`. Then,
` x+ 1 = 1/(x-(1//2)) = 2/(2x-1)`
` or (x+1)(2x-1)=2`
` or 2x^(2) + x - 3 = 0`
` or 2x^(2) + 3x - 2x - 3 = 0`
` or (x-1)(2x+3) = 0`
`rArr x = 1 " "(x =- 3//2" is rejected" )`
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