MathDB

6

Part of 2023 AMC 12/AHSME

Problems(1)

Log Midpoint

Source: 2023 AMC 12A #6

11/9/2023
Points AA and BB lie on the graph of y=log⁡2xy=\log_{2}x. The midpoint of AB‾\overline{AB} is (6,2)(6, 2). What is the positive difference between the xx-coordinates of AA and BB?
<spanclass=′latex−bold′>(A)</span> 211<spanclass=′latex−bold′>(B)</span> 43<spanclass=′latex−bold′>(C)</span> 8<spanclass=′latex−bold′>(D)</span> 45<spanclass=′latex−bold′>(E)</span> 9<span class='latex-bold'>(A)</span>~2\sqrt{11}\qquad<span class='latex-bold'>(B)</span>~4\sqrt{3}\qquad<span class='latex-bold'>(C)</span>~8\qquad<span class='latex-bold'>(D)</span>~4\sqrt{5}\qquad<span class='latex-bold'>(E)</span>~9
AMCAMC 122023 AMC2023 AMC 12Alogarithmsgraph