7.071. $3 \cdot 5^{2 x-1}-2 \cdot 5^{x-1}=0.2$.
## Solution.

From the condition $3 \cdot 5^{2 x}-2 \cdot 5^{x}=1,3 \cdot 5^{2 x}-2 \cdot 5^{x}-1=0$. Solving this equation as a quadratic in terms of $5^{x}$, we get $5^{x}=-\frac{1}{3}, \varnothing$; or $5^{x}=1$, from which $x=0$.

Answer: 0.