Question

If $3\log 2-2\log 3$ is $\log \left(\frac{m}{9}\right)$, then the value of $m$ will be

• A. $3$
• B. $6$
• C. $9$
• D. $8$

Answer 1

The correct option is D $8$

$3\log 2-2\log 3$

$=\log 2^3-\log 3^2$ ....($\because b\log a=\log a^b$)

$=\log \left(\frac{2\times 2\times 2}{3\times 3}\right)$ ...$(\because \log a-\log b=\log \frac{a}{b})$

$=\log \left(\frac{8}{9}\right)$