Question

If $\frac{{log}_{10}8}{{log}_{10}2}=?$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

$\frac{{\log }_{10}8}{{\log }_{10}2}={\log }_{2}8$ since $\frac{\log a}{\log b}={\log }_{b}a$

$={\log }_2{2}^3$

$=3{\log }_{2}2$ since $\log a^m=m\log a$

$=3$ since ${\log }_{a}a=1$