A) \[log5\]
B) \[log2\]
C) \[log6\]
D) \[\log 10\]
Correct Answer: D
Solution :
[d] \[\because 3\log 2+\frac{1}{4}-\frac{1}{2}{{\left( \frac{1}{4} \right)}^{2}}+\frac{1}{3}.{{\left( \frac{1}{4} \right)}^{3}}+......\] \[=3\log 2+\log \left( 1+\frac{1}{4} \right)\] \[\left[ \because \log (x+1)=x-\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}+......\infty \right]\] \[=3\log 2+\log \left( \frac{5}{4} \right)=3\log 2+\log 5-2\log 2\] \[=31og2+log5=\log 10\] Hence option [d] is correct.
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