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2023 AMC 12B Question 7

AMC12 · 2023 AMC 12B

Question 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?
  1. $900$
  2. $3$
  3. $902$
  4. $2$
  5. $901$