SATHEE: Theory of Equations 1 Question 26

Theory of Equations 1 Question 26

27. The number of solutions of $\log_{4} (x - 1) = \log_{2} (x - 3)$ is

(a) 3

(b) 1

(d) 0

(2001, 2M)

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Answer:

Correct Answer: 27. (b)

Solution:

Given, $\log_{4} (x - 1) = \log_{2} (x - 3) = \log_{4^{1 / 2}} (x - 3)$

$\begin{aligned} \Rightarrow & \log_{4} (x - 1) = 2 \log_{4} (x - 3) \\ \Rightarrow & \log_{4} (x - 1) = \log_{4} (x - 3)^{2} \\ \Rightarrow & (x - 3)^{2} = x - 1 \\ \Rightarrow & x^{2} + 9 - 6 x = x - 1 \\ \Rightarrow & x^{2} - 7 x + 10 = 0 \\ \Rightarrow & (x - 2) (x - 5) = 0 \\ \Rightarrow & x = 2, or x = 5 \\ \Rightarrow & x = 5 [∵ x = 2 makes log (x - 3) undefined] . \end{aligned}$

Hence, one solution exists.

Theory of Equations 1 Question 26

27. The number of solutions of $\log_{4} (x - 1) = \log_{2} (x - 3)$ is

Answer:

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Theory of Equations 1 Question 26

27. The number of solutions of log4⁡(x−1)=log2⁡(x−3) is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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27. The number of solutions of $\log_{4} (x - 1) = \log_{2} (x - 3)$ is