\[(a)\;\frac{1}{x} \log \bigg|\frac{\log x-3}{\log x-2}\bigg|\quad (b)\;\log \bigg|\frac{\log x-3}{\log x-2}\bigg|\quad (c)\;\log \bigg|\frac{\log x-2}{\log x-3}\bigg| \quad (d)\;\log |(\log x-3)(\log x-2)| \]