Question:

The number of solutions of log2(x – 1) = 2 log2(x – 3) is

Updated On: Apr 18, 2024
  • (A) 2
  • (B) 1
  • (C) 6
  • (D) 7
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The Correct Option is B

Solution and Explanation

Explanation:
Given, log2⁡(x−1)=2log2⁡(x−3)⇒log2⁡(x−1)=log2⁡(x−3)2⇒x−1=(x−3)2⇒x−1=x2+9−6x⇒x2−7x+10=0⇒(x−2)(x−5)=0⇒x=2,5since, x=2 does not satisfy the equation. So, x=5 is the only solution. Hence, number of solution is one.x=2 does not satisfy the equation as RHS becomes undefined.

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