Explanation

(a)
$\log_{0.3}{(x - 1) < \log_{0.09}(x - 1)}$
Here, $x - 1 > 0$
And $\log_{0.3}{(x - 1) < \log_{(0.3)^{2}}{(x - 1)}}$
$\Rightarrow x > 1$ and $\log_{0.3}{(x - 1) < \frac{1}{2}\log_{0.3}{(x - 1)}}$
$\Rightarrow x > 1$ and $\log_{0.3}{(x - 1) < 0}$
$\Rightarrow x > 1$ and $x - 1 > 1$
$\Rightarrow x > 1$ and $x > 2$
$\therefore\ \ \ \ x \in (2,\ \infty)$