Question

The value of $lo{g}_{10}2+16lo{g}_{10}\frac{16}{15}+12lo{g}_{10}\frac{25}{24}+7lo{g}_{10}\frac{81}{80}$ is

• A. 3
• B. 2
• C. 1
• D. 0

Answer 1

Answer: (C)

1

$Wecanwritethegivenexpressionas{log}_{10}2+{log}_{10}{\left(\frac{2^4}{3\times 5}\right)}^{16}+{log}_{10}{\left(\frac{5^2}{2^3\times 3}\right)}^{12}+{log}_{10}{\left(\frac{3^4}{2^4\times 5}\right)}^7=lo{g}_{10}\frac{2^{65}\times 5^{24}\times 3^{28}}{3^{16}\times 5^{16}\times 3^{12}\times 2^{36}\times 2^{28}\times 5^7}=lo{g}_{10}\frac{2^{65}\times 5^{24}\times 3^{28}}{2^{64}\times 5^{23}\times 3^{28}}=log5\times 2={log}_{10}10=1\left(Ans\right)$