A) 0
B) \[lo{{g}_{10}}6\]
C) \[lo{{g}_{10}}5\]
D) None of these
Correct Answer: B
Solution :
(b): \[{{\log }_{10}}\left( \frac{3}{2} \right)+{{\log }_{10}}\left( \frac{4}{3} \right)+{{\log }_{10}}\left( \frac{5}{4} \right)+.......+10th\,\]term \[={{\log }_{10}}\left( \frac{3}{2} \right)+{{\log }_{10}}\left( \frac{4}{3} \right)+{{\log }_{10}}\left( \frac{5}{4} \right)+.......{{\log }_{10}}\left( \frac{12}{11} \right)\] \[={{\log }_{10}}\left( \frac{3}{2}\times \frac{4}{3}\times \frac{5}{4}\times .....\times \frac{12}{11} \right)\] \[={{\log }_{10}}\left( \frac{12}{2} \right)={{\log }_{10}}6\]
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