Complex Numbers And Quadratic Equations question 753
Question: The number of solutions of $ {\log_4}(x-1)={\log_2}(x-3) $ [IIT Screening 2001]
Options:
A) 3
B) 1
C) 2
D) 0
Show Answer
Answer:
Correct Answer: B
Solution:
$ {\log_4}(x-1)={\log_2}(x-3) $
$ \Rightarrow x-1={{(x-3)}^{2}} $
$ \Rightarrow x^{2}-7x+10=0 $
$ \Rightarrow (x-5)(x-2)=0 $
$ \therefore x=5, $ 2 but $ x-3<0 $ when $ x=2 $
$ \therefore $ only solution is $ x=5 $
$ \therefore $ Hence number of solution is one.
BETA
