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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_6 / Points A and B lie on the graph of y=log₂x. The midpoint of (AB)¯ is (6,2). What is the positive difference between the x-coordinates of A and B? The final answer can be written in…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Points

A

and

B

lie on the graph of

y=\log_{2}x

. The midpoint of

\overline{AB}

(6, 2)

. What is the positive difference between the

x

-coordinates of

A

and

B

? The final answer can be written in the form

m \sqrt{n}

, where

m

and

n

are relatively prime positive integers. What is

m+n

Plain-text mathematical notation (without MathML)

Points A and B lie on the graph of y=log₂x. The midpoint of (AB)¯ is (6,2). What is the positive difference between the x-coordinates of A and B? The final answer can be written in the form m√(n), where m and n are relatively prime positive integers. What is m+n?

Original LaTeX notation

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 $B$? The final answer can be written in the form $m \sqrt{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_6
task_id: 1981fafe-2ed7-5ca2-a9ba-895e6bc04643
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f6
task_revision_id: 2
config / split: default / train

Official source

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