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Source: 2023 AMC 12B #7

November 15, 2023
AMC 12AMC2023 AMC 12B2023 AMClogarithms

Problem Statement

For how many integers nn does the expression log⁡(n2)−(log⁡n)2log⁡n−3\sqrt{\frac{\log (n^2) - (\log n)^2}{\log n - 3}} represent a real number, where log denotes the base 1010 logarithm? <spanclass=′latex−bold′>(A)</span>900<spanclass=′latex−bold′>(B)</span>2<spanclass=′latex−bold′>(C)</span>902<spanclass=′latex−bold′>(D)</span>2<spanclass=′latex−bold′>(E)</span>901 <span class='latex-bold'>(A) </span>900 \qquad <span class='latex-bold'>(B) </span>2\qquad <span class='latex-bold'>(C) </span>902 \qquad <span class='latex-bold'>(D) </span> 2 \qquad <span class='latex-bold'>(E) </span>901
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