Решите уравнение

log3 (2x+1) + log3 (x-1) = 1+log3 (5+x)

log₃ (2x+1) + log₃ (x-1) = 1+log₃ (5+x)

ОДЗ:

2x+1>0

x-1 >0

5+x>0

log₃ (2x+1) + log₃ (x-1) = log₃3+log₃ (5+x)

log₃ (2x+1) * (x-1) = log₃3 * (5+x)

(2x+1) * (x-1) = 3 * (5+x)

2x²-2x+х-1=15+3x

2x²-4x-16=0 : 2

x²-2x-8=0

D=4+32=36

x₁ = (2+6) / 2=4

x₂ = (2-6) / 2=-2

ответ: х=4