Rút gọn biểu thức \(p = \log {a \over b} + \log {b \over c} + \log {c \over d} - \log {{ay} \over {dx}}\).

* Hướng dẫn giải

Ta có: \(p = \log \dfrac{a}{b} + \log \dfrac{b}{c} + \log \dfrac{c}{d} - \log \dfrac{{ay}}{{dx}} \)

\(= \log \left( {\dfrac{{abc}}{{bcd}}} \right) - \left( {\log \dfrac{a}{d} + \log \dfrac{y}{x}} \right)\)

\( = \log \left( {\dfrac{a}{d}} \right) - \left( {\log \dfrac{a}{d} + \log \dfrac{y}{x}} \right) \)

\(=  - \log \dfrac{y}{x} = \log \dfrac{x}{y}.\)