Question

$lo{g}_{3}4lo{g}_{4}5lo{g}_{5}6lo{g}_{6}7lo{g}_{7}8lo{g}_{8}9$

Answer 1

${\log }_{3}4{\log }_{4}5{\log }_{5}6{\log }_{6}7{\log }_{7}8{\log }_{8}9=\frac{\log 4}{\log 3}\times \frac{\log 5}{\log 4}\times \frac{\log 6}{\log 5}\times \frac{\log 7}{\log 6}\times \frac{\log 8}{\log 7}\times \frac{\log 9}{\log 8}=\frac{\log 9}{\log 3}=\frac{\log 3^2}{\log 3}=\frac{2\log 3}{\log 3}=2$