Explanation

(b)
We have, $x^{\log_{x}(1 - x)^{2}} = 9\$
Taking log on both sides, we get
$\log_{x}(9) = \log_{x}(1 - x)^{2}$ $(\because a^{x} = N \Rightarrow \log_{a}{N = x)}$
$\Rightarrow 9 = \ (1 - x)^{2}$
$\Rightarrow 1 + x^{2} - 2x - 9 = 0$
$\Rightarrow x^{2} - 2x - 8 = 0$
$\Rightarrow x = - 2,\ 4$
$\Rightarrow x = 4$ $(\because x = - 2)$