Question

lg(3 – х) – lg(x + 2) = 2 lg 2

Answer 1

ОДЗ 3-x>0⇒x<3  U x+2>0⇒x>-2⇒x∈(-2;3)
lg(3-x)/(x+2)=lg4
(3-x)/(x+2) -4=0
(3-x-4x-8)/(x+2)=0
-5x=5
x=-1

Answer 2

ОДЗ:
3-x>0
x<3

x+2>0
x>-2

x∈(-2;3)

$lg(3-x)-lg(x+2)=2lg2\\lg(\frac{3-x}{x+2})=lg2^2\\\frac{3-x}{x+2}=4\\3-x=4(x+2)\\3-x=4x+8\\5x=-5\\\boxed{x=-1}$