7.225. $\log _{3 x+7}(5 x+3)+\log _{5 x+3}(3 x+7)=2$.
Solution.

Domain of definition: $\left\{\begin{array}{l}0-\frac{3}{5}, x \neq-\frac{2}{5}\right.$.

Multiplying the equation by $\log _{3 x+7}(5 x+3) \neq 0$, we get

$$
\begin{aligned}
& \log _{3 x+7}^{2}(5 x+3)-2 \log _{3 x+7}(5 x+3)+1=0 \Leftrightarrow\left(\log _{3 x+7}(5 x+3)-1\right)^{2}=0 \Leftrightarrow \\
& \Leftrightarrow \log _{3 x+7}(5 x+3)=1 \Leftrightarrow 5 x+3=3 x+7, x=2 \\
& \text { Answer: } 2 .
\end{aligned}
$$