Question

If $a\log x-b\log y=2\log 3$ and $x^a=m{y}^b$, then value of $m$ is equal to

• A. $9$
• B. $3$
• C. $-3$
• D. $2$

Answer 1

The correct option is A $9$

$a\log x-b\log y=2\log 3$

$\therefore \log x^a-\log y^b=\log 3^2$ ...($\log a^b=b\log a$)

$\therefore \log \frac{x^a}{y^b}=\log 9$ ...($\log \frac{a}{b}=\log a-\log b$)

$\therefore \frac{x^a}{y^b}=9$

$\therefore x^a=9y^b$