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

1.	Solve ` log_(4)(x-1)= log_(2) (x-3)`.
Answer» Correct Answer - x = 5 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`.

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