ПОМОГИТЕ РЕШИТЬ УРАВНЕНИЯ. Created by DomnikaMaksimova. algebra-ru

ПОМОГИТЕ РЕШИТЬ УРАВНЕНИЯ...

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ПОМОГИТЕ РЕШИТЬ УРАВНЕНИЯ

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nKrynka Решение
1. 2^(3x) = 3
log₂ [2^(3x)] = log₂ 3
3x = log₂ 3
x = (log₂ 3) / 3
2. (1/3)^(5 + 4x) = 3/2
3^(- 5 - 4x) = 3/2
3^(5 + 4x) = 2/3
4x + 5 = - lg(3/2) / lg3
4x = - 5 - lg(3/2)/lg3
x = - 5 - lg(3/2) / 4lg3
3. log₅ x * log₃ x = 9*log₅ 3
lg² x / [lg3 * lg5] = 9lg3/lg5
lg² x = 9lg² 3
1) lg x = 3*lg 3
lg x = lg 3³
x = 27
2) lg x = - 3*lg 3
lg x = lg 3⁻³
x = 1/27
Ответ: x₁ = 27; x₂ = 1/27
4. lg(x + 6) - lg√(2x - 3) = lg4
lg [(x + 6) / √(2x - 3) = lg4
(x + 6) / √(2x - 3) = 4
x + 6 = 4√(2x - 3)

[4√(2x - 3)]² = (x + 6)²
x + 6 ≥ 0, x ≥ - 6

16*(2x - 3) = x² + 12x + 36
32x - 48 = x² + 12x + 36
x² - 20 x + 84 = 0
D = 400 - 4*1*84 = 64
x₁ = (20 - 8)/2
x₁ = 6
x₂ = (20 + 8)/2
x₂ = 14
Ответ: x₁ = 6 ; x₂ = 14
5. log₀,₅ (x + 2) - log₂ (x - 3) = (1/2)log₂⁻¹/² (- 4x - 8)
- log₂ (x + 2) - log₂ (x - 3) = - log₂ (- 4x - 8)
log₂ [(x + 2)*(x - 3)] = log₂ (- 4x - 8)
ОДЗ: x + 2 > 0, x > - 2
x - 3 > 0. x > 3
- 4x - 8 > 0
-4x > 8
x < - 2
x² - x - 6 = - 4x - 8
x² + 3x + 2 = 0
x₁ = - 2 не удовлетворяет ОДЗ
x₂ = - 1
Ответ: x = - 1

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