A) \[{{\log }_{e}}10\]
B) \[3\,\,{{\log }_{e}}4\]
C) \[2\,{{\log }_{e}}5\]
D) \[{{\log }_{e}}\,8\]
Correct Answer: A
Solution :
\[3\,{{\log }_{e}}2+\frac{1}{4}-\frac{1}{2}.\frac{1}{{{4}^{2}}}+\frac{1}{3}.\frac{1}{{{4}^{3}}}-.....\] \[=3\,{{\log }_{e}}\,2+{{\log }_{e}}\left( 1+\frac{1}{4} \right)\] \[=3\,{{\log }_{e}}\,2+\log \,\,\frac{5}{4}\] \[=\,{{\log }_{e}}\,\left( 8.\frac{5}{4} \right)\] \[=\,{{\log }_{e}}\,10\]
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