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Omni-MATH / Let ⊗ be a binary operation that takes two positive real numbers and returns a positive real number. Suppose further that ⊗ is continuous, commutative (a⊗b=b⊗a), distributive acros…

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problem

Let ⊗\otimes be a binary operation that takes two positive real numbers and returns a positive real number. Suppose further that ⊗\otimes is continuous, commutative (a⊗b=b⊗a)(a \otimes b=b \otimes a), distributive across multiplication (a⊗(bc)=(a⊗b)(a⊗c))(a \otimes(b c)=(a \otimes b)(a \otimes c)), and that 2⊗2=42 \otimes 2=4. Solve the equation x⊗y=xx \otimes y=x for yy in terms of xx for x>1x>1.
Plain-text mathematical notation (without MathML)
Let ⊗ be a binary operation that takes two positive real numbers and returns a positive real number. Suppose further that ⊗ is continuous, commutative (a⊗b=b⊗a), distributive across multiplication (a⊗(bc)=(a⊗b)(a⊗c)), and that 2⊗2=4. Solve the equation x⊗y=x for y in terms of x for x>1.
Original LaTeX notation
Let $\otimes$ be a binary operation that takes two positive real numbers and returns a positive real number. Suppose further that $\otimes$ is continuous, commutative $(a \otimes b=b \otimes a)$, distributive across multiplication $(a \otimes(b c)=(a \otimes b)(a \otimes c))$, and that $2 \otimes 2=4$. Solve the equation $x \otimes y=x$ for $y$ in terms of $x$ for $x>1$.

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Source and history

task_id
04348dcc-9c5a-5695-bb87-a4a1a19388a6
task_key
test--04348dcc-9c5a-5695-bb87-a4a1a19388a6
task_revision_id
1
config / split
/ test

Official source

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