Решение
1)Log4(5x+6)=0
ОДЗ: 5x + 6 > 0, x > - 6/5, x > - 1 (1/5)
5x + 6 = 4°
5x + 6 = 1
5x = - 5
x = - 1
Ответ: х = - 1
2) Lg2x+lg(x+3)=lg(12x-4)
ОДЗ: x> 0;
x + 3 > 0, x > - 3
12x - 4 > 0, x > 1/3
D(y) = (1/3 ; + ∞)
Lg (2x)*(x+3) = lg(12x-4)
2x(x + 3) = 12x - 4
2x² + 6x - 12x + 4 = 0
2x² - 6x + 4 = 0
x² - 3x + 2 = 0
x1 = 1
x2 = 2
Ответ: x1 = 1; x2 = 2
4)Log1/5(7x+1/25)=2
ОДЗ: 7x + 1/25 > 0
7x > - 1/25, x > - 1 / 175
7x+1/25 = (1/5)²
7x = 1/25 - 1/25
7x = 0
x = 0
Ответ: х = 0