Explanation

(a)
$7\log_{2}{\frac{16}{15} + 5\log_{2}{\frac{25}{24} + 3\log_{2}\frac{81}{80}}}$
$= 7\left\lbrack 4\log_{2}{2 - \log_{2}{3 - \log_{2}5}} \right\rbrack + 5\left\lbrack 2\log_{2}{5 - \log_{2}{3 - 3\log_{2}2}} \right\rbrack + 3\lbrack 4\log_{2}{3 - 4\log_{2}{2 - \log_{2}5}}\rbrack$
$= \log_{2}{2 = 1}$