14. Решите уравнение 2 logo,3²x - 7 logo,3 x - 4

Решим уравнение 2log₀.₃² x - 7log₀.₃ x - 4 = 0

Пусть log₀.₃ x = t

2t² - 7t - 4 = 0

D = 49 - 4 * 2 * (-4) = 49 + 32 = 81

t₁ = (7 + 9) / 4 = 16/4 = 4

t₂ = (7 - 9) / 4 = -2/4 = -1/2

log₀.₃ x = 4

x₁ = (0.3)⁴ = 0.0081

log₀.₃ x = -1/2

x₂ = (0.3)⁻¹/² = 1 / √(0.3) ≈ 1 / 0.5477 ≈ 1.8257

Ответ: x₁ = 0.0081, x₂ ≈ 1.8257