Question

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

• A. $-2$
• B. $-1$
• C. $1$
• D. $3$

Answer 1

The correct option is C $1$

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