Explanation

(c)
Since, $\log(1 + x) - \log(1 - x)$
$= 2\left\lbrack x + \frac{x^{3}}{3} + \frac{x^{5}}{5} + ...\infty \right\rbrack$
Put $x = \frac{1}{2}$ on both sides, we get
$\log\left( \frac{3}{2} \right) - \log\left( \frac{1}{2} \right)$
$= 2\left( \frac{1}{2} + \frac{1}{3}.\frac{1}{2^{3}} + \frac{1}{5}.\frac{1}{2^{5}} + ...\infty \right)$
$\Rightarrow \ \log 3 = 1 + \frac{1}{3}.\frac{1}{4} + \frac{1}{5}.\frac{1}{4^{2}} + ...$