Question

Evaluate : ${\log }_{9}27-{\log }_{27}9$

Answer 1

${\log }_{9}27-{\log }_{27}9$

$=\frac{\log 27}{\log 9}-\frac{\log 9}{\log 27}$

$=\frac{3\log 3}{2\log 2}-\frac{2\log 3}{3\log 3}$

$=\frac{3}{2}-\frac{2}{3}$

$=\frac{9-4}{6}$

$=\frac{5}{6}$