Solve ` log_(4)(x-1)= log_(2) (x-3)`.

Answer

x = 5

Explanation

The given equality meaningful if
` x- 1 gt 0, x - 3 gt 0 rArr x gt 3`.
The given equality can be written as
` (log(x-1))/(log 4) =(log(x-3))/(log 2) `
` or log(x-1)= 2 log(x-3)(log 4 = 2 log 2)`
` or (x-1)=(x-3)^(2)`
` or x^(2) - 7x + 10 = 0`
` or (x-5)(x-2)=0`
` or x= 5 or 2`.
But ` x gt 3, so x = 5`.