The value of ${\log }_{4}27\cdot {\log }_{9}32\cdot {\log }_{125}9\cdot {\log }_{81}25$ is

$\begin{array}{l}{\log }_{4}27\cdot {\log }_{9}32\cdot {\log }_{125}9\cdot {\log }_{81}25\\ =3{\log }_{4}3\cdot 5{\log }_{9}2\cdot 2{\log }_{125}3\cdot 2{\log }_{81}5\\ =60\frac{1}{2{\log }_{3}2}\cdot \frac{1}{2{\log }_{2}3}\cdot \frac{1}{4{\log }_{5}3}\cdot \frac{1}{3{\log }_{3}5}\end{array}$
$=\frac{5}{4}$