Question

The solution set of the equation $x^{lo{g}_x(1-x{)}^2}=9$ is?

• A. $\{-2,4\}$
• B. $\left\{4\right\}$
• C. $\{0,-2,4\}$
• D. None of these

Answer 1

Answer: (B)

$\left\{4\right\}$

$x^{{\log }_x(1-x{)}^2}$

$\Rightarrow {\log }_x(1-x{)}^2={\log }_{x}9$

$\Rightarrow (1-x{)}^2=9$

$\Rightarrow 1-x=3$

$x=-2$ (It is not possible).

$\Rightarrow 1-x=-3$

$\Rightarrow x=4$

$\therefore x=4$