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log(3/4)log8(x^2+7)+log(1/2)log(1/4)(x^2...

`log_(3/4)log_8(x^2+7)+log_(1/2)log_(1/4)(x^2+7)^(-1)=-2`.

Text Solution

Verified by Experts

The correct Answer is:
`pm3`
`log_(3//4)log_(8)(x^(2)+7)+log_(1//2)log_(1//4)(x^(2)+7)^(-1)=-2`
`rArr log_(3//4)((1)/(3)log_(2)(x^(2)+7))-log_(2)(log_(2)(x^(2)+7))/(2)=-2`
Let `log_(2)(x^(2)+7)=t`
`rArr "log"_(3//4)(t)/(3)-"log"_(2)(t)/(2)+2=0`
`rArr "log"_(3//4)(t)/(3)+1-("log"_(2)(t)/(2)-1)=0`
`rArr "log"_(3//4)(t)/(4)="log"_(2)(t)/(4)`
`rArr (t)/(4)=1`
`rArr t = 4`
`rArr log_(2)(x^(2)+7)=4`
`rArr x^(2)+7=16`
`rArr x^(2)=9`
`rArr x^(2)= pm 3`
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