Explanation

(c)
Let $x_{1},x_{2},\ x_{3},\ldots,\ x_{n}$ be the variates corresponding to $n$ sets of data, each having the same number of observations say $k$ and $x$ be their product. Then, $x = x_{1},\ x_{2},\ldots,x_{n}$
$\log x = \log x_{1} + \log x_{2} + \ldots + \log x_{n}$
$\Rightarrow \frac{\sum_{}^{}{\log x}}{k} = \frac{\sum_{}^{}{\log x_{1}}}{k} + \frac{\sum_{}^{}{\log x_{2}}}{k} + \ldots + \frac{\sum_{}^{}{\log x_{n}}}{k}$
$\Rightarrow \ \log G = \log G_{1} + \log G_{2} + \ldots + \log G_{n}$
$\Rightarrow G = G_{1}G_{2},\ldots,G_{n}$