27.23. Compare the numbers $\log _{5} 7$ and $\log _{13} 17$.
27.23. It is clear that $\log _{5} 7-1=\log _{5} \frac{7}{5}$ and $\log _{13} 17-1=\log _{13} \frac{17}{13}$. It is easy to verify that $\frac{7}{5}>\frac{17}{13}$. Therefore, $\log _{5} \frac{7}{5}>\log _{13} \frac{7}{5}>\log _{13} \frac{17}{13}$. In the end, we get that $\log _{5} 7>\log _{13} 17$.