1) log 6 (9-6x+x²) = 2 2) 2lgx>lg (4x+21)

1.

log6 (9 - 6x + x²) = 2; 9 - 6x + x² = 6^2; 9 - 6x + x² - 36 = 0; x² - 6x - 27 = 0; D/4 = (b/2) ^2 - ac; D/4 = (-3) ^2 - 1 * (-27) = 9 + 27 = 36; x = (-b/2 ± √ (D/4)) / a; x1 = 3 - 6 = - 3; x2 = 3 + 6 = 9.

2.

1) ОДЗ:

{x > 0;

{4x + 21 > 0; {x > 0;

{4x > - 21; {x > 0;

{x > - 21/4; x ∈ (0; ∞).

2) Преобразуем неравенство:

2lgx > lg (4x + 21); lg (x^2) > lg (4x + 21); x^2 > 4x + 21; x^2 - 4x - 21 > 0.

3) Корни трехчлена:

D/4 = 2^2 + 21 = 25; x = 2 ± √25 = 2 ± 5; x1 = 2 - 5 = - 3; x2 = 2 + 5 = 7.

4) Решение неравенства:

{x ∈ (0; ∞);

{x ∈ (-∞; - 3) ∪ (7; ∞); x ∈ (7; ∞).