1) log5 (4x+17) = log5 (x4-3) + 1

2) log3 (2x+1) = log3 (13) + 1

3) log3 (x^2-3) + log3 (2) = log3 (6x-10)

1) log5 (4x+17) = log5 (4x-3) + 1 ОДЗ 4 х-7>0 x>7/4,4x-3>0 x>3/4

log₅ (4x+17) = log₅ (4x-3) + log₅ 5

log5 (4x+17) = log5 (4x-3) * 5

log5 (4x+17) = log5 (20x-15)

4 х+17=20 х-15

16 х=32

х=2

log₃ (2x+1) = log₃ (13) + log₃ 3 ОДЗ 2 х+1>0 x> - 1/2

log₃ (2x+1) = log₃ (13*3)

log₃ (2x+1) = log₃39

2x+1=39

2x=38

x=14

3) log₃ (x²-3) + log₃ (2) = log₃ (6x-10) ОДЗ х ²-3>0 x>√3, x<-√3

6x-10>0 x>5/3

log₃ (x²-3) * 2=log₃ (6x-10)

2x²-6=6x-10

2x²-6x+4=0 / 2

x²-3x+2=0

D=9-8=1

x₁ = (3+1) / 2=2

x₂ = (3-1) / 2=1 не подходит под ОДЗ