Example 2. Solve the equation

$$
(0.4)^{x-1}=(6.25)^{6x-5}
$$
Solution. Since

$$
\begin{gathered}
(0.4)^{x-1}=(2 / 5)^{x-1} \\
(6.25)^{6 x-5}=(25 / 4)^{6 x-5}=(5 / 2)^{12 x-10}=(2 / 5)^{10-12 x}
\end{gathered}
$$

then

$$
(2 / 5)^{x-1}=(2 / 5)^{10-12 x} \Leftrightarrow x-1=10-12 x \Leftrightarrow x=11 / 13
$$

When solving simple exponential equations, a transformation is used that involves factoring out a common factor.