MathDB

Log Midpoint

Source: 2023 AMC 12A #6

November 9, 2023

AMCAMC 122023 AMC2023 AMC 12Alogarithmsgraph

Problem Statement

Points

A

and

B

lie on the graph of

y=\log_{2}x

. The midpoint of

\overline{AB}

is

(6, 2)

. What is the positive difference between the

x

-coordinates of

A

and

B

?

<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

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