Question

In(x²-6x+9)=In3+In(x+3)

Answer 1

ln(x^2 - 6x + 9) = ln3 + ln(x + 3)
ОДЗ: 
{x² - 6x + 9 > 0, (x - 3)² > 0;  ( -∞; 3)∪(3; + ∞) 
{x + 3 > 0; x > - 3
x ∈ (- 3; 3)∪(3; + ∞)
ln(x² - 6x + 9) = ln(3*(x + 3))
x² - 6x + 9 = 3*(x + 3)
x² - 6x + 9 = 3x + 9
x² - 9x = 0
x*(x - 9) = 0
x₁ = 0
x - 9 = 0
x₂ = 9