${\log _3}\,4{\log _4}\,5{\log _5}\,6{\log _6}\,7{\log _7}\,8{\log _8}\,9= . .$ . .
IIT 2000, Easy
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b
(b) \({\log _3}4.{\log _4}5.{\log _5}6.{\log _6}7.{\log _7}8.{\log _8}9\)
(b) \({\log _3}4.{\log _4}5.{\log _5}6.{\log _6}7.{\log _7}8.{\log _8}9\)
\( = {{\log 4} \over {\log 3}}.{{\log 5} \over {\log 4}}.{{\log 6} \over {\log 5}}.{{\log 7} \over {\log 6}}.{{\log 8} \over {\log 7}}.{{\log 9} \over {\log 8}} = {{\log 9} \over {\log 3}}\)
\( = {\log _3}9 = {\log _3}{3^2} = 2\).
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