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

Answer

`x=2,1- sqrt(23)`

Explanation

`(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)`