7.204. $\sqrt[4]{|x-3|^{x+1}}=\sqrt[3]{|x-3|^{x-2}}$.

7.204. $\sqrt[4]{|x-3|^{x+1}}=\sqrt[3]{|x-3|^{x-2}}$.
Solution.

Obviously, $x \neq 3$, then $|x-3|>0$. Rewrite the equation as $|x-3|^{\frac{x+1}{4}}=|x-3|^{\frac{x-2}{3}}$

We get two cases:

$$
\begin{aligned}
& \text { 1) }|x-3|=1 \Rightarrow x_{1}=2, x_{2}=4 \\
& \text { 2) }|x-3| \neq 1 \Rightarrow \frac{x+1}{4}=\frac{x-2}{3} \Leftrightarrow 3 x+3=4 x-8, x_{3}=11
\end{aligned}
$$

Answer: $2 ; 4 ; 11$.