3. (1984 National High School Competition) The number of real roots of the equation $\sin x=\lg x$ is $(\quad)$.
A. 1
B. 2
C. 3
D. Greater than 3
3. C. Reason: The number of solutions to the equation $\sin x=\lg x$ is the number of intersection points between the sine curve $\sin x$ and the logarithmic curve $\lg x$. First, determine the range of $x$. From the definition of $\lg x$, we know: $x>0$, and since $\sin x \leqslant 1$, it follows that $\lg x \leqslant 1$, i.e., $0 < x \leq 10$. Since $\sin 1 > 0$ and $\lg 1 = 0$, and $\sin \pi=0$, it is clear that when $x \in(1, \pi)$, $\sin x=\lg x$ must have one solution. Similarly, it can be known that when $x \in\left(2 \pi, 2 \pi+\frac{\pi}{2}\right)$ and $x \in\left(2 \pi+\frac{\pi}{2}, 3 \pi\right)$, the equation has one solution each, so the equation $\sin x=\lg x$ has 3 real roots.