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 $I$
• C. is a finite set containing at least two elements
• D. a finite set

Answer 1

Answer: (A), (B), (D)

a subset of $R$ containing $I$
$a$ subset of $R$ containing $N$
a finite set

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

$\Rightarrow lo{g}_x(1-x{)}^2\left({\log }_{x}x\right)=\log 9\cdots \cdots [\because a^{{\log }_{a}b}=b]$
$\Rightarrow \log (1-x{)}^2=\log 9\cdots \cdots [\because {\log }_{a}a=1]$
$\Rightarrow (1-x{)}^2=9$
$\Rightarrow x=-2,4$
Since, $x>0$
Therefore, $x\in \left\{4\right\}$
Ans: A,B,D