Q. The solution set of the equation $x^{\log_{x}(1 - x)^{2}} = 9$ is
A) $\{ - 2,\ 4\}$
B) {4}
C) $\{ 0,\ - 2,\ 4\}$
D) None of these
Explanation
(b)
$x^{\log_{x}(1 - x)^{2}} = 9$
$\Rightarrow \ \ 9 = (1 - x)^{2}$
$\Rightarrow \ \ \ x^{2} - 2x - 8 = 0$
$\Rightarrow (x + 2)(x - 4) = 0$
$\Rightarrow x = 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lbrack\because x \neq - 2\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.