(c) ${\log _{0.04}}(x – 1) \ge {\log _{0.2}}(x – 1)$ …..$(i)$

For log to be defined $x – 1 > 0 \Rightarrow x > 1$

From $(i),$ ${\log _{{{(0.2)}^2}}}(x – 1) \ge {\log _{0.2}}(x – 1)$

$ \Rightarrow $${1 \over 2}{\log _{0.2}}(x – 1) \ge {\log _{0.1}}(x – 1)$

$ \Rightarrow $$\sqrt {x – 1} \le (x – 1)$

$ \Rightarrow $$\sqrt {x – 1} (1 – \sqrt {x – 1} ) \le 0$ $ \Rightarrow $$1 – \sqrt {x – 1} \le 0$

$ \Rightarrow $$\sqrt {x – 1} \ge 1$ $ \Rightarrow $$x \ge 2$,

$\therefore \,\,x \in [2,\,\infty )$ .