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Source: 2018 AMC 12B #7

February 16, 2018
AMCAMC 12AMC 12 B

Problem Statement

What is the value of
log⁡37⋅log⁡59⋅log⁡711⋅log⁡913⋯log⁡2125⋅log⁡2327? \log_37\cdot\log_59\cdot\log_711\cdot\log_913\cdots\log_{21}25\cdot\log_{23}27?
<spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>3log⁡723<spanclass=′latex−bold′>(C)</span>6<spanclass=′latex−bold′>(D)</span>9<spanclass=′latex−bold′>(E)</span>10<span class='latex-bold'>(A) </span> 3 \qquad <span class='latex-bold'>(B) </span> 3\log_{7}23 \qquad <span class='latex-bold'>(C) </span> 6 \qquad <span class='latex-bold'>(D) </span> 9 \qquad <span class='latex-bold'>(E) </span> 10
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