{"status": "success", "data": {"description_md": "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?\n\n$\\textbf{(A) }900 \\qquad \\textbf{(B) }3\\qquad \\textbf{(C) }902 \\qquad \\textbf{(D) } 2  \\qquad \\textbf{(E) }901$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>For how many integers  <span class=\"katex--inline\">n</span>  does the expression <span class=\"katex--display\">\\sqrt{\\frac{\\log (n^2) - (\\log n)^2}{\\log n - 3}}</span> represent a real number, where log denotes the base  <span class=\"katex--inline\">10</span>  logarithm?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }900 \\qquad \\textbf{(B) }3\\qquad \\textbf{(C) }902 \\qquad \\textbf{(D) } 2  \\qquad \\textbf{(E) }901</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2023 AMC 12B Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc12B_p08", "prev": "/problem/23_amc12B_p06"}}