Question 22
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 $x \gt 1$.