1) lg (x^2+12x+28) - lg (x+4) = 0 2) log1/3 (6-3x) >-2 Система log3 (x-y) = 4 log2x+log2y=1+log2 41

1.

lg (x^2 + 12x + 28) - lg (x + 4) = 0;

lg (x^2 + 12x + 28) = lg (x + 4);

x^2 + 12x + 28 = x + 4;

x^2 + 11x + 24 = 0;

x = (-11 ± √ (121 - 96)) / 2 = (-11 ± 5) / 2;

1) x = - 8 ∉ ОДЗ (x + 4 < 0);

2) x = - 3 - корень.

2.

log (1/3) (6 - 3x) > - 2;

{6 - 3x > 0;

{6 - 3x < (1/3) ^ (-2) - т. к. 1/3 < 1;

{3x < 6;

{6 - 3x < 9;

{3x < 6;

{3x > - 3;

{x < 2;

{x > - 1;

x ∈ (-1; 2).

3.

{log3 (x - y) = 4;

{log2 (x) + log2 (y) = 1 + log2 (41);

{x - y = 3^4;

{log2 (xy) = log2 (82);

{x + (-y) = 81;

{x * (-y) = - 82.

x и - y - корни уравнения:

t^2 - 81t - 82 = 0;

t1 = - 1; t2 = 82.

1)

{x = - 1;

{-y = 82;

{x = - 1;

{y = - 82 ∉ ОДЗ (x, y < 0).

2)

{x = 82;

{-y = - 1

{x = 82;

{y = 1.