Question

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

• A. $\log 3$
• B. $\log 5$
• C. $\log 7$
• D. $\log 2$

Answer 1

The correct option is D $\log 2$

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

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

$=[\log \left(\frac{3^{12}}{2^{12}{5}^3}\right)+\log \left(\frac{5^{10}}{2^{15}{3}^5}\right)+\log \left(\frac{2^{28}}{3^7{5}^7}\right)]$

$=\log \left[\frac{3^{12}{5}^{10}{2}^{28}}{2^{27}{3}^{12}{5}^{10}}\right]$

$=log2$