(4) Let the roots of the equations $\log _{4} x-\left(\frac{1}{4}\right)^{x}=0$ and $\log _{\frac{1}{4}} x-\left(\frac{1}{4}\right)^{x}=0$ be $x_{1}$ and $x_{2}$, respectively, then ( ).
(A) $0<x_{1} x_{2}<1$
(B) $x_{1} x_{2}=1$
(C) $1<x_{1} x_{2}<2$
(D) $x_{1} x_{2} \geqslant 2$
(4) A Hint: Clearly $x_{2}=\frac{1}{2}$. Let $f(x)=\log _{4} x-\left(\frac{1}{4}\right)^{x}$, then $f(1)$. $f(2)<0$, so $1<x_{1}<2$.