Question

If $3^{x+1}=6^{{\log }_{2}3}$, then $x$ is equal to

• A. $3$
• B. $2$
• C. ${\log }_{3}2$
• D. ${\log }_{2}3$

Answer 1

The correct option is D ${\log }_{2}3$

$3^{x+1}=6^{{\log }_{2}3}=3^{{\log }_{2}6},[\because x^{{\log }_{a}y}=y^{{\log }_{a}x}]$
Equating the power of $3$
$x+1={\log }_{2}6={\log }_2(3\times 2)={\log }_{2}3+{\log }_{2}2=1+{\log }_{2}3$
$\therefore x={\log }_{2}3$
Ans: D