Explanation

(b)
Given, $a^{x} = b^{y} = c^{z} = m$(say)
$\Rightarrow \ \ \ x = \log_{a}{m,\ \ \ y = \log_{b}{m,\ \ \ \ z = \log_{c}m}}$
Again as, $x,\ y,\ z$ are in GP, so
$\frac{y}{x} = \frac{z}{y}$
$\Rightarrow \ \frac{\log_{b}m}{\log_{a}m} = \frac{\log_{c}m}{\log_{b}m}$
$\Rightarrow \ \frac{\log_{m}a}{\log_{m}b} = \frac{\log_{m}b}{\log_{m}c}$
$\Rightarrow \log_{b}{a = \log_{c}b}$