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Multiplying Logarithms

Source: AMC 12 A #9

November 11, 2021
logarithms

Problem Statement

A right rectangular prism whose surface area and volume are numerically equal has edge lengths log⁡2x\log_2 x, log⁡3x\log_3 x, and log⁡4x\log_4 x. What is xx? <spanclass=′latex−bold′>(A)</span>26<spanclass=′latex−bold′>(B)</span>66<spanclass=′latex−bold′>(C)</span>24<spanclass=′latex−bold′>(D)</span>48<spanclass=′latex−bold′>(E)</span>576<span class='latex-bold'>(A) </span>2\sqrt{6}\qquad<span class='latex-bold'>(B) </span>6\sqrt{6}\qquad<span class='latex-bold'>(C) </span>24\qquad<span class='latex-bold'>(D) </span>48\qquad<span class='latex-bold'>(E) </span>576
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