Question

The value of $7\log \left(\frac{16}{15}\right)+5\log \left(\frac{25}{24}\right)+3\log \left(\frac{81}{80}\right)$ is

• A. $0$
• B. $\log 2$
• C. $\log 3$
• D. $\log 5$

Answer 1

The correct option is B $\log 2$

$7\log \left(\frac{16}{15}\right)+5\log \left(\frac{25}{24}\right)+3\log \left(\frac{81}{80}\right)$
$=7(\log 16-\log 15)+5(\log 25-\log 24)+3(\log 81-\log 80)$
$=7(4\log 2-\log 5-\log 3)+5(2\log 5-3\log 2-\log 3)+3(4\log 3-4\log 2-\log 5)$
$=\log 2$