Explanation

(c)
Given, $\log{(1 + 3x + 2x^{2})}$
$= \log(1 + x) - \log(1 + 2x)$
$= \left( x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - \frac{x^{4}}{4} + ... \right) + \left( 2x - \frac{(2x)^{2}}{2} + \frac{(2x)^{3}}{3} - ... \right)$
$= 3x - \frac{5}{2}x^{2} + \frac{9}{3}x^{3} - \frac{17}{4}x^{4} + ...$