A) \[\log 2+\log 3\]
B) \[\log 2+2\]
C) \[\frac{1}{2}\log 2\]
D) \[\log 3\]
Correct Answer: D
Solution :
\[\log 2+2\left( \frac{1}{5}+\frac{1}{3}\cdot \frac{1}{{{5}^{3}}}+\frac{1}{5}\cdot \frac{1}{{{5}^{5}}}+...\infty \right)\] \[=\log 2+\log \left( \frac{1+\frac{1}{5}}{1-\frac{1}{5}} \right)\] \[=\log 2+\log \left( \frac{3}{2} \right)=\log 3\]
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