4. The real root of the equation $\sin x=\lg x$ is
(A) 1 ;
(B) 2 ;
(C) 3 ;
(D) greater than 3 .
4. (C)

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 $\lg x$,
$$
\begin{array}{l}
x>0 \text {, and } \quad \sin x \leqslant 1, \\
\therefore \quad \lg x \leqslant 1, \quad \therefore 0 < x \leq 10, \\
\text { Since } \sin \pi=0, \\
\therefore \quad \text { when } x \in(1, \pi) \text {, there must be one solution to } \sin x=\lg x, 
\end{array}
$$

Similarly,
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 in each interval, so the equation $\sin x=\lg x$ has 3 real roots.