Solution:

Since $|\sin| \le 1,$ solutions need $x \in \left[\tfrac{1}{20}, 20\right],$ where $\log_{20} x$ rises from $-1$ to $1.$ The curve $\sin(20\pi x)$ has period $\tfrac{1}{10},$ and on every full monotonic branch inside this interval it crosses the slowly increasing log exactly once. There are $398$ such full branches; the partial branch near $x = \tfrac{1}{20}$ adds one crossing, while the partial branch near $x = 20$ adds none (the sine cannot rise to the log's near-$1$ value there). This gives $399$ solutions.

Thus, the correct answer is D.