7.205. $|x-3|^{3 x^{2}-10 x+3}=1$.

7.205. $|x-3|^{3 x^{2}-10 x+3}=1$.
## Solution.

Obviously, $x \neq 3$, hence $|x-3|>0$. Taking the logarithm of both sides of the equation with base 10, we have $\left(3 x^{2}-10 x+3\right) \lg |x-3|=0$, from which $3 x^{2}-10 x+3=0$ or $\lg |x-3|=0$. The roots of the quadratic equation $3 x^{2}-10 x+3=0$ are $x_{1}=\frac{1}{3}$ and $x_{2}=3$. From the equation $\lg |x-3|=0$ we find $|x-3|=1 \Rightarrow x-3=-1$ or $x-3=1$. Then $x_{3}=2, x_{4}=4 ; x_{2}=3$ does not satisfy the domain of the logarithm.

Answer: $\frac{1}{3} ; 2 ; 4$.