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  4. If log3x + log3y = 2 + log32 and log3(x + y) = 2, then

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Q. If $\log_3x + \log_3y = 2 + \log_32$ and $\log_3(x + y) = 2$, then

WBJEEWBJEE 2011

Solution:

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