110 In $\triangle A B C$, $\lg \tan A+\lg \tan C=2 \lg \tan B$, then the range of $B$ is
A. $0<B \leqslant \frac{\pi}{3}$
B. $\frac{\pi}{3} \leqslant B<\frac{\pi}{2}$
C. $\frac{\pi}{2}<B \leqslant \frac{3}{2} \pi$
D. $\frac{3}{2} \pi<B \leqslant 2 \pi$
110 B. Clearly, $A$, $B$, and $C$ are all acute angles.
From the given, we have $\tan ^{2} B=\tan A \tan C \leqslant\left(\frac{\tan A+\tan C}{2}\right)^{2}$, thus
$$
\begin{array}{l} 
2 \tan B \leqslant \tan A+\tan C=\tan (A+C)(1-\tan A \tan C) \\
=-\tan B\left(1-\tan ^{2} B\right) \\
\therefore \quad \tan ^{2} B \geqslant 3, \tan B \geqslant \sqrt{3}, \\
\therefore \quad \frac{\pi}{3} \leqslant B<\frac{\pi}{2} .
\end{array}
$$