Question

If $x{\log }_{3}a=y{\log }_{9}a$, then the value of $x$ will be

• A. $2y$
• B. $y$
• C. $\frac{1}{2}y$
• D. None of these

Answer 1

Answer: (C)

$\frac{1}{2}y$

We have,
$x{\log }_{3}a=y{\log }_{9}a$
$\Rightarrow x\frac{\log a}{\log 3}=y\frac{\log a}{\log 3^2},[\because {\log }_{x}y=\frac{\log y}{\log x}]$
$\Rightarrow x\frac{\log a}{\log 3}=y\frac{\log a}{2\log 3}$
$\therefore x=\frac{y}{2}$