Với \(m = {\log _6}2\), \(n = {\log _6}5\) thì \({\log _3}5\)bằng

\({\log _x}w = 12\)\( \Rightarrow {\log _w}x = \frac{1}{{12}}\)

\({\log _y}w = 20\)\( \Rightarrow {\log _w}y = \frac{1}{{20}}\).

Lại do

\({\log _{xyz}}w = 6\)\( \Leftrightarrow \frac{1}{{{{\log }_{_w}}\left( {xyz} \right)}} = 6\)\( \Leftrightarrow \frac{1}{{{{\log }_{_w}}x + {{\log }_{_w}}y + {{\log }_{_w}}z}} = 6\)\( \Leftrightarrow \frac{1}{{{{\log }_{_w}}x + {{\log }_{_w}}y + {{\log }_{_w}}z}} = 6\)

\( \Leftrightarrow \frac{1}{{\frac{1}{{12}} + \frac{1}{{20}} + {{\log }_{_w}}z}} = 6\)\( \Leftrightarrow {\log _{_w}}z = \frac{1}{{30}}\)\( \Rightarrow {\log _z}w = 30\).