Explanation

(c)
$2\tanh^{- 1}{\left( \frac{1}{2} \right) = \tanh^{- 1}\frac{2\left( \frac{1}{2} \right)}{1 + \left( \frac{1}{2} \right)^{2}} = \tanh^{- 1}\frac{4}{5}}$
$\left\lbrack \because\ 2\tanh^{- 1}{x = \tanh^{- 1}\frac{2x}{1 + x^{2}}} \right\rbrack$
$= \frac{1}{2}\log{\left( \frac{1 + \frac{4}{5}}{1 - \frac{4}{5}} \right) = \frac{1}{2}\log 3^{2}}$
$= \log 3$