Log3(x-2)+log3(x+6)=2 Help me!!

Question

Log3(x-2)+log3(x+6)=2
Help me!!

Answer 1

Log3(x-2)+log3(x+6)=2       ОДЗ: х≥2
log_3((x-2)(x+6))=2
(x-2)(x+6)=3²
x²+4x-12=9
x²+4x-21=0
x₁+x₂=-4
x₁*x₂=-21
x₁=-7 - лишний корень
x₂=3
х=3