7.210. $5^{x-1}+5 \cdot 0.2^{x-2}=26$.
## Solution.

Let's rewrite the equation as

$$
\frac{5^{x}}{5}+\frac{125}{5^{x}}-26 \doteq 0 \Leftrightarrow 5^{2 x}-130 \cdot 5^{x}+625=0
$$

Solving it as a quadratic equation in terms of $5^{x}$, we get $\left(5^{x}\right)_{1}=5$ or $\left(5^{x}\right)_{2}=5^{3}$, from which $x_{1}=1, x_{2}=3$.

Answer: $1 ; 3$.