Question

Express $\log \frac{26}{51}-\log \frac{91}{119}$ in terms of $\log 2$ and $\log 3$

• A. $\log 2+\log 3$
• B. $\log 2-\log 3$
• C. $\log 3-2\log 2$
• D. $2\log 2+\log 3$

Answer 1

Answer: (B)

$\log 2-\log 3$

Let $\log \frac{26}{51}$$-$ $\log \frac{91}{119}=x$
$\therefore \log \left(\frac{\frac{26}{51}}{\frac{91}{119}}\right)=x$ ($\log \frac{a}{b}=\log a-\log b$)

The value of $\frac{26}{51}\times \frac{119}{91}=\frac{2}{3}$

$\therefore x=\log \frac{2}{3}$

$\therefore x=\log 2-\log 3$