Solve : `(3)/(2)log_(4)(x+2)^(2)+3=log_(4)(4-x)^(3)+log_(4)(6+x)^(3)`.

1.	Solve : `(3)/(2)log_(4)(x+2)^(2)+3=log_(4)(4-x)^(3)+log_(4)(6+x)^(3)`.
Answer» Correct Answer - `x=2,1- sqrt(23)` `(3)/(2)log_(4)(x+2)^(2)+3=log_(4)(4-x)^(3)+log_(4)(6+x)^(3)` `rArr 3=log_(4)((24-2x-x^(2))/(\|x+2\|))^(3)` `rArr ((24-2x-x^(2))/(\|x+2\|))^(3)=4^(3)` `rArr (24-2x-x^(2))/(\|x+2\|)=4` If `x+2gt0` `rArr x^(2)+6x-16=0` `rArr (x-2)(x+8)=0` `rArr x = 2` If `x+2 lt 0` `x^(2)-2x-32 =0` `rArr x=1 - sqrt(33)`

Discussion

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