4. For a function $f(x)$ defined on the interval $[a, b]$, if there exists a constant $c$, such that for any $x_{1} \in[a, b]$ there is a unique $x_{2} \in[a, b]$, satisfying $\frac{f\left(x_{1}\right)+f\left(x_{2}\right)}{2}=c$, then the function $f(x)$ is said to have a "mean" of $c$ on $[a, b]$. Then, the mean of the function $f(x)=\lg x$ on $[10,100]$ is ( ).
(A) 10
(B) $\frac{1}{10}$
(C) $\frac{3}{2}$
(D) $\frac{3}{4}$