Question

$\log \left(\frac{75}{16}\right)-2\log \frac{5}{9}+\log \left(\frac{32}{243}\right)$

• A. $\log 3$
• B. $\log 2$
• C. $\log 5$
• D. None of these

Answer 1

The correct option is B $\log 2$

Now, the equation can be written as

$\log \frac{75}{16}$ $+$ $\log \frac{81}{25}$ $+$ $\log \frac{32}{243}$

Using Product property of $\log$, we have

$\log$ $[$$\frac{75}{16}$ $\times \frac{81}{25}$ $\times \frac{32}{243}$ $]$

$\log$ $\left(\frac{75\times 81\times 32}{16\times 25\times 243}\right)$

$=\log \left(2\right)$