1) lg (5-x)+lgx=lg4; 2) lg (x+1)+lg(x-1)=lg3; 3) ln (6-x)+lnx=ln5; 4) lgx+lg

1)lg(5 - x) + lgx = lg4.
Используя свойство логарифма произведения:
lg((5-x) * х) = lg4.
(5 - x) * х = 4.
x2 - 5x + 4 = 0.
D = 25 - 4 * 1 * 4 = 9.
D = 3.
Т.к. D gt; 0, то корней два.
x1 = (5 + 3) / 2 = 4.
x2 = (5 - 3) / 2 = 1.
2)ln(6 - x) + lnx = ln5.
ln((6 - x) * x) = ln5.
(6 - x) * x = 5.
x2 - 6x + 5 = 0.
D=36 - 4 * 1 * 5 = 16.
D = 4.
x1 = (6 + 4) / 2 = 5.
x2 = (6 - 4) / 2 = 1.
3)lg(x + 1) + lg(x - 1) = lg3.
lg((x + 1)(x - 1)) = lg3.
(x + 1)(x - 1) = 3.
x2 - 1 = 3.
x2 = 4.
x1= -2. Не подходит т.к. -2 - 3 = - 5, а lg(-5) не имеет смысла по определению.
x2 = 2.
4)lgx + lg(x - 3) = 1.
lg(x(x - 3)) = lg10.
x(x - 3) = 10.
x2 - 3x - 10 = 0.
D = 9 - 4 * 1 * 10 = 49.
x1 = (3 + 7) / 2 = 5.
x2 = (3 - 7) / 2 = -2. Не подходит.