Помогите с алгеброй, пожалуйста. Created by Sem9910. algebra-ru

Помогите с алгеброй, пожалуйста...

June 2022 1 7 Report

Помогите с алгеброй, пожалуйста

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nKrynka Решение
1) 6*log₆₄ (-x) = 5
ОДЗ: - x > 0, x < 0
log₆₄ (- x) = 5/6
- x = 64⁵/⁶
- x = (2⁶)⁵/⁶
- x = 2⁵
x = - 32
2) log₁/₂ (1/6x + 3) = 1
ОДЗ: 1/6 * x + 3 > 0
x > - 18
(1/6)*x + 3 = (1/2)¹
(1/6)*x = - 3 + 1/2
x = - 2,5*6
x = - 15
3) log₇¹/² (x² - 1) = 4
x² - 1 = (7¹/²)⁴
x² = 49 + 1
x² = 50
x₁= - 5√2
x₂= 5√2
4) log₂(₅)¹/² (- x² - 9x) = 2
ОДЗ: - x² - 9x > 0
x² + 9x < 0
x(x + 9) < 0
x₁ = 0
x₂ = - 9
x ∈(- 9; 0)
- x² - 9x = (2√5)²
- x² - 9x - 20 = 0
x² + 9x + 20 = 0
x₁ = - 4
x₂ = - 5
5) log₄ x + log₃ x = log₁₆ 2
lgx/lg4 + lgx/lg3 = 1/4
[lg(3) + lg(4)]*lg(x) / (lg(3)*lg(4)) = 1/4
lg(x) = [lg(3)*lg(4)] / 4*[lg(3) + lg(4)]
x = e^[(lg3)*lg(4)] / [4*(lg(3) + lg(4)]

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