A) {- 2, 4}
B) {4}
C) {0, - 2, 4}
D) None of these
Correct Answer: A
Solution :
\[{{x}^{{{\log }_{x}}(1-x)}}^{2}=9\] Þ \[{{\log }_{x}}(9)={{\log }_{x}}{{(1-x)}^{2}}(\because {{a}^{x}}=N\,\,\,\Rightarrow {{\log }_{a}}N=x)\] Þ \[9={{(1-x)}^{2}}\,\,\,\Rightarrow 1+{{x}^{2}}-2x-9=0\] Þ \[{{x}^{2}}-2x-8=0\]Þ \[(x+2)(x-4)=0\] Þ \[x=-2\,,4\].
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