4. The real root of the equation $\sin x=\lg x$ is
(A) 1
(B) 2
(C) 3
(D) Greater than 3
(C)
4. 【Analysis and Solution】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 $x$. By the definition of logarithms,
$$
\begin{array}{l}
x>0 \text {, and } \sin x \leqslant 1, \\
\therefore \lg x \leqslant 1, \therefore 0 < x \leqslant 10.
\end{array}
$$
Since $\sin \pi=0$,
$$
\begin{array}{l}
\therefore \text { when } x \in(1, \pi), \sin x=\lg x \text { must have one solution. Similarly, when } x \in\left(2 \pi, 2 \pi+\frac{\pi}{2}\right) \text { and } x \in\left(2 \pi+\frac{\pi}{2}, 3 \pi\right), \\
\text { the equation has one solution in each interval. Therefore, the equation } \sin x=\lg x \text { has 3 real roots.}
\end{array}
$$