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Let (log(x)(2a-x))/(log(x)2)+(log(a)(x))...

Let `(log_(x)(2a-x))/(log_(x)2)+(log_(a)(x))/(log_(a)2)=(1)/(log_(a^(2)-1)2)`. Then sum of possible value(s) of `a` for which equation has only one solution, willlie in interval

A

`(0,e)`

B

`(e,2e)`

C

`(log_(2)7,log_(2)17)`

D

`(log_(2)3,log_(2)9)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`log_(2)(2a-x)+log_(2)x=log_(2)(a^(2)-1)`
`x^(2)-2ax+a^(2)=1`
`x-a=+-1`
`x=a+1` or `x=a-1`
`x` will have only one solution iif `a-1=1`
`impliesa=2` as for `a=2` x not be equal to 1
so `x=a+1` is only solution `a=2`
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