Question

The value of $\frac{1}{{\log }_{3}60}+\frac{1}{{\log }_{4}60}+\frac{1}{{\log }_{5}60},$ is

Answer 1

$\frac{1}{{\log }_{3}60}+\frac{1}{{\log }_{4}60}+\frac{1}{{\log }_{5}60}$
$={\log }_{60}3+{\log }_{60}4+{\log }_{60}5$
$={\log }_{60}(3\times 4\times 5)$
$={\log }_{60}60$
$=1$