Question
Mathematics Question on Maxima and Minima
The number of solutions of log2(x – 1) = 2 log2(x – 3) is
A
(A) 2
B
(B) 1
C
(C) 6
D
(D) 7
Answer
(B) 1
Explanation
Solution
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.