3. The function
$$
f(x)=\log _{\frac{1}{16}} x-\left(\frac{1}{16}\right)^{x}
$$

has the number of zeros ( ).
(A) 0
(B) 1
(C) 2
(D) 3
3. D.

The required is the number of intersection points of the graph of the function $y=\log _{16} x$ and the graph of the function $y=\left(\frac{1}{16}\right)^{x}$ for $x>0$.

It is easy to know that the graph of the function $y=\log _{\frac{1}{16}} x$ and the graph of the function $y=\left(\frac{1}{16}\right)^{x}$ are symmetric about $y=x$. Therefore, there must be a point $(a, a)$ on the graphs of these two functions.

Upon verification, the points $\left(\frac{1}{2}, \frac{1}{4}\right)$ and $\left(\frac{1}{4}, \frac{1}{2}\right)$ are also intersection points of the two graphs.
Thus, the number of zeros is 3.