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
The expression y = ax2 + bx + c has always the same sign as c if -...If product of roots of the equation x2 − 4mx + 3e2 log m − 4 = 0 is 8, then its roots are real, when m equal...The number of real solutions of the equation = 3√3 is -...Let a, b, c be real numbers, a ≠ 0. If α is a root of a2x2 + bx + c = 0, β is the root of a2x2 - bx - c ...How many roots does the equation $x^{3} + ax + 2 = 0$ possess depending on ' $a$ '?...