8. $\left\{\begin{array}{l}|x-2 a| \leq 3 \\ \log _{2}(x+a) \leq 2\end{array} \Leftrightarrow\left\{\begin{array}{l}-5 \leq x-2 a \leq 5 \\ 0<x+a \leq 4\end{array} \Leftrightarrow\left\{\begin{array}{l}2 a-5 \leq x \leq 2 a+5 \\ -a<x \leq 4-a\end{array}\right.\right.\right.$

Let's represent the obtained inequalities with shading on the number line.

Then the system will have a unique solution if

![](https://cdn.mathpix.com/cropped/2024_05_06_62b84f4e75df73adcd4cg-6.jpg?height=106&width=731&top_left_y=2240&top_left_x=345)
$2 a-5=4-a$, that is, $a=3$. In this case, the unique solution will be $x=1$.
Answer: $\mathrm{a}=3, \mathrm{x}=1$.

## 4 variant.