Question

Value of $(\log \frac{75}{16}-2\log \frac{5}{9}+\log \frac{32}{243})$ is ?

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

Answer 1

Answer: (D)

$\log 2$

$\log \frac{75}{16}-2\log \frac{5}{9}+\log \frac{32}{243}=\log \frac{75}{16}-\log {\left(\frac{5}{9}\right)}^2+\log \frac{32}{243}=\log \frac{75}{16}-\log \frac{25}{81}+\log \frac{32}{243}=\log \left(\frac{\frac{75}{16}}{\frac{25}{81}}\right)+\log \frac{32}{243}=\log \frac{243}{16}+\log \frac{32}{243}=\log \frac{243}{16}.\frac{32}{243}=\log 2$