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AIME 2024 / AIME 2024 train a33d1f18-7e90-5a1f-a45a-30efd708f220

Problem

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

Problem

There exist real numbers

x

and

y

, both greater than 1, such that

\log_x\left(y^x\right)=\log_y\left(x^{4y}\right)=10

. Find

xy

Plain-text mathematical notation (without MathML)

There exist real numbers x and y, both greater than 1, such that log_(x)(y^(x))=log_(y)(x^(4y))=10. Find xy.

Original LaTeX notation

There exist real numbers $x$ and $y$, both greater than 1, such that $\log_x\left(y^x\right)=\log_y\left(x^{4y}\right)=10$. Find $xy$.

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Source and history

task_id: a33d1f18-7e90-5a1f-a45a-30efd708f220
task_key: default--train--a33d1f18-7e90-5a1f-a45a-30efd708f220
task_revision_id: 2
config / split: default / train

Official source

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