Question

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

Answer 1

$7log\left(\frac{16}{15}\right)+5log\left(\frac{25}{24}\right)+3log\left(\frac{81}{80}\right)$
$\because alogx=log{x}^a$
$\Rightarrow log(\frac{16}{15}{)}^7+log(\frac{25}{24}{)}^5+log(\frac{81}{80}{)}^3$
$\because logx+logy=log(x\times y)$
$\Rightarrow log(\frac{{16}^7}{{15}^7}.\frac{{25}^5}{{24}^5}.\frac{{81}^3}{{80}^3})$
$=log2$