Description for Correct answer:
We have, \( \Large x^{logx \left(1-x\right)^{2} }=9 \)

Taking log on both sides, we get

\( \Large x \left(9\right)=log x \left(1-x\right)^{2} \left(\because a^{x}=N => log a N = x \right) \)

=> \( \Large 9= \left(1-x\right)^{2} => 1+x^{2}-2x-9=0 \)

=> \( \Large x^{2}-2x-8=0 \)

=> \( \Large x = -2, 4 \)

=> \( \Large x = 4 \left(\because x = 2\right) \)