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].
Create a free account to view solution
View Solution FreeMore Quadratic Equation Questions
Let $M = 3x^{2} - 8xy + 9y^{2} - 4x + 6y + 13$, where $x,y \in R$, then...Let f (x) be a quadratic expression which is positive for all real values of x.If g (x) = f(x) + f′(x) + f′&...The diagram shows the graph of y = ax2 + bx + c. Then -...If 2 + 3i is one of the roots of the equation 2x3 − 9x2 + kx − 13 = 0, k ∈ R, then the real root of th...The roots of the equation x4 - 8x2 - 9 = 0 are-...