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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_11 / What is the product of all real numbers x such that the distance on the number line between log₆x and log₆9 is twice the distance on the number line between log₆10 and 1?

Problem

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

problem

What is the product of all real numbers

x

such that the distance on the number line between

\log_6x

and

\log_69

is twice the distance on the number line between

\log_610

and

1

Plain-text mathematical notation (without MathML)

What is the product of all real numbers x such that the distance on the number line between log₆x and log₆9 is twice the distance on the number line between log₆10 and 1?

Original LaTeX notation

What is the product of all real numbers $x$ such that the distance on the number line between $\log_6x$ and $\log_69$ is twice the distance on the number line between $\log_610$ and $1$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_11
task_id: b7d30393-cede-535c-b13b-4f3a12f94610
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12A~5fProblems~2fProblem~5f11
task_revision_id: 2
config / split: default / train

Official source

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