3. If the real numbers $x, \alpha, \beta$ satisfy
$$
x=\log _{3} \tan \alpha=-\log _{3} \tan \beta \text {, and } \alpha-\beta=\frac{\pi}{6} \text {, }
$$

then the value of $x$ is $\qquad$ .
3. $\frac{1}{2}$.

Let $\tan \alpha=y$. Then $\tan \beta=\frac{1}{y}$, $\tan \beta=\tan \left(\alpha-\frac{\pi}{6}\right)=\frac{y-\frac{1}{\sqrt{3}}}{1+\frac{y}{\sqrt{3}}}$. Therefore, $\frac{1}{y}=\frac{y-\frac{1}{\sqrt{3}}}{1+\frac{y}{\sqrt{3}}}$.
Taking the positive root gives $y=\sqrt{3}$.
Thus, $x=\log _{3} y=\frac{1}{2}$.