Complex Numbers And Quadratic Equations question 724
Question: The solution set of the equation $ {x^{{\log_{x}}{{(1-x)}^{2}}}}=9 $ is [Pb. CET 2003]
Options:
A) {- 2, 4}
B) {4}
C) {0, - 2, 4}
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ {x^{{\log_{x}}(1-x)}}^{2}=9 $
Þ $ {\log_{x}}(9)={\log_{x}}{{(1-x)}^{2}}(\because a^{x}=N\Rightarrow {\log_{a}}N=x) $
Þ $ 9={{(1-x)}^{2}}\Rightarrow 1+x^{2}-2x-9=0 $
Þ $ x^{2}-2x-8=0 $
Þ $ (x+2)(x-4)=0 $
Þ $ x=-2,4 $ .
BETA
