1) log5 x + logx 5 = 2,5

2) lg^2 x-2 lg x^2 + 3 = 0

1) log₅ x + logₓ 5 = 2,5 ОДЗ х>0

log₅ x + (1/log₅ x) = 2,5

log²₅ x - 2,5 log₅ x + 1=0

2log²₅ x - 5 log₅ x + 2=0 log₅ x=a

2a²-5a+2=0

D=25-16=9

a = (5+3) / 4=2 log₅ x=2 x₁=5²=25

a = (5-3) / 4=1/2 log₅ x = 1/2 x₂=√5

2) lg^2 x-2 lg x^2 + 3 = 0 ОДЗ х>0

lg^2 x-4 lg x + 3 = 0 lg x=a

a²-4a+3=0

D=16-12=4

a = (4+2) / 2=3 lg x=3 x₁=10³=1000

a = (4-2) / 2=1 lg x=1 x₂=10