Question

Find the value of $\frac{{\log }_{10}72}{{\log }_{10}8}$ using log table

• A. ${\log }_{10}9$
• B. $1+\frac{.954}{.903}$
• C. $2$
• D. $\frac{.903+.954}{.954}$

Answer 1

The correct option is B $1+\frac{.954}{.903}$

$\frac{{\log }_{10}72}{{\log }_{10}8}=\frac{{\log }_{10}(8\times 9)}{{\log }_{10}8}=\frac{{\log }_{10}8+{\log }_{10}9}{{\log }_{10}8}$

$=1+\frac{{\log }_{10}{3}^2}{{\log }_{10}{2}^3}=1+\frac{2{\log }_{10}3}{3{\log }_{10}2}$

$=1+\frac{2.\left(0.477\right)}{3.\left(0.301\right)}=1+\frac{\left(0.954\right)}{\left(0.903\right)}$