Question

Solve $lo{g}_{3}x+lo{g}_{3}y=2+lo{g}_{3}2,lo{g}_{27}(x+y)=\frac{2}{3}$

Answer 1

$lo{g}_3\left(\frac{xy}{2}\right)=2$ from 1st
$\therefore \frac{xy}{2}=3^{2}orxy=18$
$x+y=(3^3{)}^{2/3}=9$ from 2nd
$\therefore x,yarerootsof{t}^2-9t+18=0$
$\therefore$ $(t-6)(t-3)=0$
$\therefore$ $(x,y)=(3,6)or(6,3)$