Question

Find the value of $\frac{{\log }_{10}64}{{\log }_{10}8}$

Answer 1

Given, $\frac{{\log }_{10}64}{{\log }_{10}8}$

$={\log }_{64}8$ using $\frac{{\log }_{a}b}{{\log }_{a}c}={\log }_{c}b$

$={\log }_{2^6}{2}^3$

$=\frac{3}{6}{\log }_{2}2$ using ${\log }_{a^n}{b}^m=\frac{m}{n}{\log }_{a}b$

$=\frac{1}{2}$ since ${\log }_{a}a=1$