2023 AMC 12B Problem 7

For how many integers n does the expression

\[ \sqrt{\frac{\log(n^2)-(\log n)^2}{\log n-3}} \]

represent a real number, where \log denotes the base 10 logarithm?

\textbf{(A)} 900 \qquad \textbf{(B)} 3 \qquad \textbf{(C)} 902 \qquad \textbf{(D)} 2 \qquad \textbf{(E)} 901

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.