5) log₁/₈ (x-4) = -1
x-4 = (1/8)⁻¹
x-4 = 8
x = 12
Ответ: 12
6) log₂.₅ (x+2) = 1
x+2 = 2.5
x = 0.5
Ответ: 0,5
7) lg x = -2
x = 10⁻²
x = 1/100 = 0.01
Ответ: 0,01
8) ln x = 1
x = e¹ = e
Ответ: е
9) log₂ (x² - 2x) = 3
ОДЗ: x² - 2x>0
x² - 2x = 2³
x² - 2x - 8 =0
D₁ = 1+8 = 9
x₁ = 4
x₂ = -2
Ответ: 4; -2
10) log₁/₅ (4x +x²) = -1
ОДЗ: 4x+x² >0
4x+x² = (1/5)⁻¹
4x + x² = 5
x² + 4x - 5 =0
x₁ = 1
x₂ = -5
Ответ: 1; -5
11) log₀.₅ (x³ + 1) = -1
x³ + 1 = (0.5) ⁻¹
x³ + 1 = 2
x³ = 1
x = 1
Ответ: 1
12) lg (7x-x²) = 1
ОДЗ: 7x - x² > 0
7x - x² = 10
-x² + 7x - 10 = 0
x² - 7x + 10 = 0
D = 49 - 40 = 9
x₁ = 5
x₂ = 2
Ответ: 5;2
13) log₃.₂ (2-x) = log₃.₂ (3x+6)
ОДЗ: 2-x>0
3x+6>0
2-x = 3x+ 6
-4x = 4
x = -1
Ответ: -1
14) log₀.₈ (1+2x) = log₀.₈ (4x-10)
1+2x = 4x - 10
-2x = -11
x = 5.5
Ответ: 5,5
15) log₂ (x-6) + log₂ (x-8) = 3
ОДЗ: x-6>0
x-8>0
log₂ ((x-6)(x-8)) = log₂8
(x-6)(x-8) = 8
x² - 8x - 6x + 48 = 8
x² - 14x + 40 = 0
D₁ = 49 - 40 = 9
x₁ = 10
x₂ = 4 не удов. ОДЗ
Ответ: 10
16) log₈ (x-2) - log₈ (x-3) = 1/3
ОДЗ: x-2>0
x-3>0
log₈ (
= log₈2
x - 2 = 2x - 6
-x = -4
x = 4
Ответ: 4