(3-lgx+lg3)lgx=2lg3+2 ...

(3-lgx+lg3)lgx=2lg3+2

 

^ -степень
(3-lgx+lg3)lgx=2lg3+2
y = lgx
(3-y+lg3)y=2lg3+2
-y^2 +(3+lg3)y - 2(lg3 +1) = 0
y^2 - (3+lg3)y + 2(lg3 +1) = 0
D = (3+lg3)^2 - 4*1*2(lg3 +1) = (lg3-1)^2
√D = -/+ (lg3-1)
y = 1/2 (3+lg3 -/+(lg3-1) )
y1 = 1/2 (3+lg3 -(lg3-1) ) =1/2 (3+lg3 -lg3+1) = 2
lgx=y1= 2
lgx = 2lg10 = lg100
x = 100
y2 = 1/2 (3+lg3 +(lg3-1) ) =1/2 (3+lg3 +lg3-1) = lg3 +1
lgx=y2= lg3+1
lgx = lg3 + 1 =lg30
x = 30
Ответ x = {30; 100}