(d) ${5^{x – 1}} + 5\,{(0.2)^{x – 2}} = 26$$ \Rightarrow $${5^{x – 1}} + 5\,.\,{\left( {{1 \over 5}} \right)^{x – 2}} = 26$

==>${5^{x – 1}} + {5^{3 – x}} = 26$$ \Rightarrow $${5^{x – 1}} + 25\,.\,{5^{ – (x – 1)}} – 26 = 0$

==>${5^{2(x – 1)}} – 26.\,{5^{(x – 1)}} + 25 = 0$

==>${5^{2(x – 1)}} – {5^{x – 1}} – {25.5^{x – 1}} + 25 = 0$

==>${5^{x – 1}}({5^{x – 1}} – 1) – 25({5^{x – 1}} – 1) = 0$

==>$({5^{x – 1}} – 25)({5^{x – 1}} – 1) = 0$ ==>$({5^{x – 1}} – {5^2})\,({5^{x – 1}} – {5^0}) = 0$

==> ${5^{x – 1}} = {5^2}$or ${5^{x – 1}} = {5^0}$$ \Rightarrow $$x = 3,\,1$.