Quadratic EquationHard
Question
The number of solutions of log4 (x - 1) = log2 (x - 3) is
Options
A.3
B.1
C.2
D.0
Solution
Given, log4(x - 1) = log2(x - 3) = log41/2(x - 3)
⇒ log4(x - 1) = 2log4(x - 3)
⇒ log4(x - 1) = log4(x - 3)2
⇒ (x - 3)2 = x - 1
⇒ x2 - 9 - 6x = x - 1
⇒ x2 - 7x + 10 = 0
⇒ (x - 2)(x - 5) = 0
⇒ x = 2 or x = 5
⇒ x = 5[∵ x = 2 makes log (x - 3) undefined].
⇒ log4(x - 1) = 2log4(x - 3)
⇒ log4(x - 1) = log4(x - 3)2
⇒ (x - 3)2 = x - 1
⇒ x2 - 9 - 6x = x - 1
⇒ x2 - 7x + 10 = 0
⇒ (x - 2)(x - 5) = 0
⇒ x = 2 or x = 5
⇒ x = 5[∵ x = 2 makes log (x - 3) undefined].
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