27.22. Compare the numbers $\log _{20} 80$ and $\log _{80} 640$.
27.22. It is clear that $\log _{20} 80=1+2 \log _{20} 2$ and $\log _{80} 640=1+3 \log _{80} 2$. Further, $\log _{20} 2=\frac{1}{\log _{2} 20}$ and $\log _{80} 2=\frac{1}{\log _{2} 80}$. Moreover, $3 \log _{2} 20=$ $=\log _{2} 8000>\log _{2} 6400=2 \log _{2} 80$. Therefore, $\log _{20} 80<\log _{80} 640$.