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Question

Find the value of: $$\displaystyle \log_{3}4.\log_{4}5.\log_{5}6.\log_{5}7.\log_{7}8.\log_{7}8.\log_{8}9.$$


Solution

$$\displaystyle \log_{3}4.\log_{4}5.\log_{5}6.\log_{5}7.\log_{7}B.\log_{7}B.\log_{8}9$$

$$\Rightarrow \displaystyle \frac{\log4 }{\log3}\times \frac{\log5}{\log4}\times \frac{\log7}{\log6}\times \frac{\log7}{\log6}\times \frac{\log8}{\log7}\times \frac{\log9}{\log8}=\frac{\log9}{\log3}=2.$$

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