Question

${log}_{10}2+{16log}_{10}\left(\frac{16}{15}\right)+{12log}_{10}\left(\frac{25}{24}\right)+{7log}_{10}\left(\frac{81}{80}\right)$

Answer 1

${\log }_{10}2+16{\log }_{10}+12{\log }_{10}\left(\frac{25}{24}\right)+7{\log }_{10}\left(\frac{81}{80}\right)$

$={\log }_{10}(2\times (\frac{16}{15}{)}^{16}\times (\frac{25}{24}{)}^{12}\times (\frac{81}{80}{)}^7)$

$={\log }_{10}(2\times 3^0\times 5)$

$={\log }_{10}10=1$