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The number of solution of log(4)(x-1) = ...

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

A

3

B

1

C

2

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
Given `log_(4)(x-1)=log_(2)(x-3)=log_(4^(1//2))(x-3)`
`implieslog_(4)(x-1)=2log_(4)(x-3)`
`implieslog_(4)(x-1)=log_(4)(x-3)^(2)`
`implies(x-3)^(2)=x-1`
`impliesx^(2)+9-6x=x-1`
`impliesx^(2)-7x+10=0`
`implies(x-2)(x-5)=0`
`impliesx-2,or x=5`
`impliesx=5 [becausex=2"makes log (x-3) underfined"].`
Hence, one solution exists.
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