Question

$\left \{ {{ 3^{x }* 3^{y} =81 } \atop {log 3}(x+y)= log_{3} x+2 log_{3} 2 }} \right.$

Answer 1

3^(x)*3^(y)=3^(x+y)=81=3^4 => x+y=4 (I)
2log3(2)=log3(4)
log3(x+y)=log3(x)+log3(4)=log3(4x)
x+y=4x => y=3x (II)
inlocuim II in I
x+3x=4x=4 => x=1 => y=3*1=3

Answer 2

81 = 3⁴                         x +y =4 
   x >0 ; y >0                x +y  = x ·4 
y=3·x                          x + 3x =4    ;  4x =4  ; x =1 
y =3