Question

Решить log0.5(x+2)+log0.5(x+3)=log0.5(3-1)

Answer 1

ОДЗ:
x + 2 > 0
x + 3 > 0
x > -3
x > -2

$log_{0,5}(x + 2)(x + 3) = log_{0,5}2 \\ \\ (x + 2)(x + 3) = 2 \\ \\ x^2 + 2x + 3x + 6 = 2\\ \\ x^2 + 5x + 4 = 0 \\ \\ x_1 + x_2 = -5 \\ x_1 \cdot x_2 = 4 \\ \\ x_1 = -1 \\ x_2 = -4 - \ ne \ \ ud.$

ответ: x = -1. 

Answer 2

log0.5(x+2)+log0.5(x+3)=log0.5(3-1)
{x+2>0⇒x>-2
{x+3>0⇒x>-3
x∈(-2;∞)
log(a)b+log(a)c=log(a)(bc)
log(0,5)[(x+2)(x+3)]=log(0,5)2
x²+5x+6=2
x²+5x+4=0
x1+x2=-5 U x1*x2=4
x1=-1 U x2=-4 не удов усл
ответ х=-1