Question

${\log }_{s}9.{\log }_9\mathrm{10......}{\log }_{3}64$

Answer 1

${\log }_{8}9\times {\log }_{9}10\times {\log }_{3}64$

$=\frac{{\log }_{10}9}{{\log }_{10}8}\times \frac{{\log }_{10}10}{{\log }_{10}9}\times \frac{{\log }_{10}64}{{\log }_{10}3}$ $[\because {\log }_{n}m=\frac{\log m}{\log n}]$

$=\frac{2{\log }_{10}8}{{\log }_{10}8}\times \frac{1}{{\log }_{10}3}[\because {\log }_{10}10=1]$

$=2{\log }_{3}10$ Ans