3. Solve the equation $3^{1-2|x|}+3 \cdot 9^{1+|x|}=82$. (4 points)
Solution:

$$
3^{2 x \mid}=t \geq 1, \quad 27 t^{2}-82 t+3=0, \quad t=3, \quad 3^{2|x|}=3, \quad 2|x|=1, \quad x= \pm \frac{1}{2} \quad \text{Answer: } x= \pm \frac{1}{2} .
$$