Question

Find the value of $\frac{{\log }_{8}17}{{\log }_{9}23}-\frac{{\log }_{3\sqrt{2}}17}{{\log }_{3}23}.$

Answer 1

$\frac{{\log }_{8}17}{{\log }_{9}23}-\frac{{\log }_{3\sqrt{2}}17}{{\log }_{3}23}$

$=\frac{{\log }_{8}17}{\frac{1}{2}{\log }_{3}23}-\frac{\frac{{\log }_{8}17}{\frac{1}{2}{\log }_{8}18}}{{\log }_{3}23}$

$=2\frac{{\log }_{8}17}{{\log }_{3}23}({\log }_{8}18-1)$

Hence, solved.