If the interval x satisfying the equation
`|x| +|-x|=(log_(3)(x-2))/(|log_(3)(x-2)|) " is " (a,b), " then " a+b=` _______.

Answer

5

Explanation

We know that
`[x]+[-x]={(-1",",x notinI),(0",",x in I):}`
and RHS is either +1 or -1
` :. ` above equation valid only when
`(log_(3)(x-2))/(|log_(3)(x-2)|)=-1`
`implies log_(3)(x-2)=` negative
`implies 0 lt x-2 lt 1`
`implies 2 lt x lt 3`
`implies x in (2, 3)`
`implies a=2, b=3`