Question

If ${\log }_{3}x+{\log }_{3}y=2+{\log }_{3}2$ and ${\log }_3(x+y)=2$, then values of $x$ and $y$ are

• A. $x=1,y=8$
• B. $x=8,y=1$
• C. $x=3,y=6$
• D. $x=9,y=3$

Answer 1

Answer: (C)

$x=3,y=6$

Given ${\log }_{3}x+{\log }_{3}y=2+{\log }_{3}2$ and ${\log }_3(x+y)=2$

${\log }_{3}xy={\log }_3{3}^2+{\log }_{3}2$

$x+y=3^2$

$\Rightarrow xy=18$

$\Rightarrow x+y=9$

$\therefore x=3;y=6$