Log₂ (x + 1) + log₂ (x + 3) = 3

Question

Log₂ (x + 1) + log₂ (x + 3) = 3

Answer 1

Решаем логарифмическое уравнение

Answer 2

Log ₂ ( X + 1 ) + log ₂ ( X + 3 ) = 3 
log ₂ ( X + 1 )*( X + 3 ) = 3 
2 ^ 3 = ( X + 1 )*( X + 3 ) 
X² + 4X  + 3 - 8 = 0 
X²+ 4X - 5 = 0
D = 16 + 20 = 36 ; √ D = 6 
X1 = ( - 4 + 6 ) : 2 = 1 
X2 = ( - 4 - 6 ) : 2 = - 5