Question

The value of $\log_{3} 4 \log_{4} 5 5 \log_{5} 6 \log_{6} 7 \log_{7} 8 \log_{8} 9$ is

Easy

Solution

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

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