Question 67
Positive real numbers $x$ and $y$ satisfy
$$
2013^{\log_3 x} = y^{\log_5 2013} \quad \text{and} \quad \log_{\frac{1}{2}} x + \log_{\frac{1}{2}} y \gt 0.
$$
Which of the numbers $x$ and $y$ is greater?
$$
2013^{\log_3 x} = y^{\log_5 2013} \quad \text{and} \quad \log_{\frac{1}{2}} x + \log_{\frac{1}{2}} y \gt 0.
$$
Which of the numbers $x$ and $y$ is greater?