Question

If $l=\log \frac{5}{7},m=\log \frac{7}{9}$ and $n=2(\log 3-\log \sqrt{5});$ then the value of $l+m+n$ will be

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

$l+m+n=\log \frac{5}{7}+\log \frac{7}{9}+2(\log 3-\log \sqrt{5})=\log \frac{5}{7}+\log \frac{7}{9}+2\log 3-2\log \sqrt{5}=\log \left(\frac{5\times 7\times 3^2}{7\times 9\times 5}\right)=\log \left(\frac{5\times 7\times 3\times 3}{7\times 9\times 5}\right)=\log 1=0$