When the function \( f(x) = \log x \) is modified to \( f(x) + 204 \), the effect on the graph is that it shifts vertically.
More specifically, adding a constant value (in this case, 204) to the function results in a vertical shift upward. Therefore, the graph of \( f(x) + 204 \) will be a vertical shift of the original graph \( f(x) = \log x \) by 204 units up.
Thus, the correct response is:
The graph shifts 204 units up.