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Question: The value of \(\log_{3}4\log_{4}5\log_{5}6\log_{6}7\log_{7}8\log_{8}9\)is...

The value of log⁡34log⁡45log⁡56log⁡67log⁡78log⁡89\log_{3}4\log_{4}5\log_{5}6\log_{6}7\log_{7}8\log_{8}9is

A

1

B

2

C

3

D

4

Answer

2

Explanation

Solution

log⁡34.log⁡45.log⁡56.log⁡67.log⁡78.log⁡89\log_{3}4.\log_{4}5.\log_{5}6.\log_{6}7.\log_{7}8.\log_{8}9

=log⁡4log⁡3.log⁡5log⁡4.log⁡6log⁡5.log⁡7log⁡6.log⁡8log⁡7.log⁡9log⁡8=log⁡9log⁡3= \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⁡39=log⁡332=2= \log_{3}9 = \log_{3}3^{2} = 2.