The number of solution of `log_(4)(x-1) = log_(2)(x-3)` is

Explanation

The given equation is
` log_(2) (x -3) = log_(22) (x-1)`
`rArr log_(2) (x-3) = (1)/(2) log_(2) (x-1)`
`rArr 2 log_(2) (x-3)=log_(2)(x-1)`
` rArr log_(2) (x-3)^(2)= log_(2) (x-1)`
`rArr x^(2) - 6x + 9 = x - 1 " "` provided ` x gt 3 and x gt 1`
` rArr x^(2) - 7x + 10 = 0 " "` where ` x gt 3`
` rArr x^(2) - 7x + 10 = 0 " "` where ` x gt 3 `
` rArr (x - 5) (x-2) = 0 " "` where `x gt 3 `
But ` 2 lt 3 ` , hence x = 5 is the onlu solution of the givne equation . Cansequently the number
of solution of the given equation is one .