Question

lg (2x + 1) = 0,5 lg(1-3x)​

Answer 1

Ответ:

lg (2x+1) = 0,5 * lg (1-3x)

ОДЗ: (2x+1)>0 и (1-3x)>0

или x>-1\2 и x<1\3

lg (2x+1) = lg (1-3x)^(0,5)

2x+1 = (1-3x)^0,5

(2x+1)^2 = 1-3x

4x^2 + 4x + 1 = 1 - 3x

4x^2 + 7x = 0

x * (4x + 7) = 0

x = 0

(4x + 7) = 0 => x = -7\4- не удовлетв. ОДЗ (x> -1\2) =>

x = 0

Объяснение:

Answer 2

ОДЗ :

$\left \{ {{2x+1>0} \atop {1-3x>0}} \right.\\\\\left \{ {{2x>-1} \atop {-3x>-1}} \right.\\\\\left \{ {{x>-0,5} \atop {x<\frac{1}{3} }} \right. \ \Rightarrow \ x\in(-0,5 \ ; \ \frac{1}{3})\\\\\\lg(2x+1)=lg(1-3x)\\\\2x+1=1-3x\\\\2x+3x=1-1\\\\5x=0\\\\\boxed{x=0}$