MathDB

9

Part of 2021 AMC 12/AHSME Fall

Problems(2)

Multiplying Logarithms

Source: AMC 12 A #9

11/11/2021
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
logarithms
Geometry Bash

Source: 12B #9

11/17/2021
Triangle ABCABC is equilateral with side length 66. Suppose that OO is the center of the inscribed circle of this triangle. What is the area of the circle passing through AA, OO, and CC?
<spanclass=′latex−bold′>(A)</span> 9π<spanclass=′latex−bold′>(B)</span> 12π<spanclass=′latex−bold′>(C)</span> 18π<spanclass=′latex−bold′>(D)</span> 24π<spanclass=′latex−bold′>(E)</span> 27π<span class='latex-bold'>(A)</span>\ 9\pi \qquad<span class='latex-bold'>(B)</span>\ 12\pi \qquad<span class='latex-bold'>(C)</span>\ 18\pi \qquad<span class='latex-bold'>(D)</span>\ 24\pi \qquad<span class='latex-bold'>(E)</span>\ 27\pi
geometryAMCAMC 12AMC 12 B