Question

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

• 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 two elements
• D. a finite set

Answer 1

The correct option is D a finite set

$x^{lo{g}_x(1-x{)}^2}=9$
above equation is valid when $x>0$,$x\ne 1$

$\Rightarrow lo{g}_x(1-x{)}^2\left(\log x\right)=\log 9$
$\Rightarrow \log (1-x{)}^2=\log 9$
$\Rightarrow (1-x{)}^2=9$
$\Rightarrow x=-2,4$
Since, $x>0$
Therefore, $x\in \left\{4\right\}$
Ans: D