Lg1/2 (3x-x^2) + √3^log 5 1<0

lg (3x²+12x+19) - lg (3x+4) = 1

ОДЗ 3 х³+12 х+19>0

D=144-228=-84<0⇒x-любое

3 х+4>0⇒x>-4/3

x∈ (-4/3; ∞)

lg (3x²+12x+19) / (3x+4) = 1

(3x²+12x+19) / (3x+4) = 10

3x²+12x+19-30x-40=0

3x²-18x-21=0

x²-6x-7=0

x1+x2=6 U x1*x2=-7⇒x1=-1 U x2=7

lg (x^2+2x-7) - lg (x-1) = 0

ОДЗ x²+2x-7>0

D=4+28=32

x1 = (-2-4√2) / 2=-1-2√2

x2=-1+2√2

x-1+2√2

x-1>0⇒x>1

x∈ (-1+2√2)

lg (x^2+2x-7) / (x-1) = 0

(x^2+2x-7) / (x-1) = 1

x²+2x-7-x+1=0

x²+x-6=0

x1+x2=-1 U x1*x2=-6

x1=-3∉ОДЗ

х2=2

log5 (x^2+8) - log5 (x+1) = 3log5 2

ОДЗ

x²+8>0⇒x-любое

x+1>0⇒x>-1

x∈ (-1; ∞)

log5 (x^2+8) / (x+1) = log5 8

(x^2+8) / (x+1) = 8

x²+8-8x-8=0

x²-8x=0

x (x-8) = 0

x=0 U x=8