Question

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

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

Answer 1

Answer: (C)

Given, ${\log }_{3}x+{\log }_{3}y=2+{\log }_{3}2$
and ${\log }_3(x+y)=2$
$\therefore {\log }_{3}xy={\log }_3{3}^2+{\log }_{3}2$
and $x+y=3^2$
$\Rightarrow xy=18$ and $x+y=9$
$\therefore x=3$ and $y=6$