Question

The set of all values of $x$ satisfying $x^{{\log }_x(1-x{)}^2}=9$ is

• A. A subset of $R$ containing $N$
• B. A subset of $R$ containing $Z$ (set of all integers).
• C. Is a finite set containing at least $2$ elements.
• D. A finite set.

Answer 1

The correct option is D A finite set.

$x^{{\log }_x(1-x{)}^2}=91-x\ne 0\Rightarrow x\ne 1\text{Also,}x>0x^{{\log }_x(1-x{)}^2}=9(1-x{)}^2=91-x=\pm 3\Rightarrow x=4\text{or}x=-2\therefore x=4$