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Let $$(x_0, y_0)$$ be the solution of the following equations$$(2x)^{\ln 2} = (3y)^{\ln 3}$$$$3^{\ln x} = 2^{\ln y}$$Then $$x_0$$ is
$$\frac{1}{6}$$
$$\frac{1}{3}$$
$$\frac{1}{2}$$
$$6$$
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