log²1/3x - log 1/3x = 2

Question

log²1/3x - log 1/3x = 2

Answer 1

ОДЗ  x > 0
log 1/3x = t 
t^2 - t - 2=0
D = -1^2 -4*1*-2 = 9
t1 =1/2 (1-3)= -1; log 1/3x = -1; (1/3)^-1 = x ; x =3
t2 =1/2 (1+3)=2 ; log 1/3x =2; (1/3)^2 = x; x =1/9
ответ x = {1/9 ; 3}