Question

If ${\log }_{3}x=3\&{\log }_{x}y=4$, then find $y$.

• A. $3^6$
• B. $3^9$
• C. $3^{12}$
• D. $none$

Answer 1

Answer: (C)

$3^{12}$

We have,

${\log }_{3}x=3$

We know that

${\log }_{a}x=y\Rightarrow x=a^y$

Therefore,

$x=3^3$

$x=27$

Here,

${\log }_{x}y=12$

$y=x^{12}$

On putting the value of $x$, we get

$y=3^{12}$

Hence, this is the answer.