Как сможете 1) log3.2 (2-x) = log3.2 (3x+6) 2) log0.8 (1+2x) = log0.8 (4x-10) 3) log2 (x-6)+ log2 (x-8) = 3 4) log8 (x-2) - log8 (x-3) = 1/3 1) lg (5-x) = 1/3lg (35-x^3) 2) log2 x-5/x+5 + log2 (x+5) = 0 3) log2 (3x-6) - 1 = log2 (9x-19) 1)log7 (x-2) + log7 (x+2) = log7 (4x+41) 2) log4 (x+1) - log4 (1-x) = log4 (2x+3) 3) log4 (x+3) - log4 (x-1) = 2 - log4 8 4) lg (x-1) + lg (x+1) = 3lg2 + lg (x-2) 1) 2 log3 (x-2) + log3 (x-4)^2 = 0 2) 2lgx - lg4 + lg (5-x^2) = 0 3) lg [x(x+9)] + lg x+9/x = 0

Ответы

ludcolobanova 02.07.2020 23:22

1) log₃.₂ (2-x) = log₃.₂ (3x+6)
2-x = 3x+6
-4x = 4
x = -1
ответ: -1
2) log₀.₈(1+2x) = log₀.₈ (4x-10)
1+2x = 4x-10
-2x = -11
x = 5.5
ответ: 5,5
3) 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 = 7+3 = 10
x₂ = 7-3 = 4 не удов. ОДЗ
ответ: 10
4) log₈ (x-2) - log₈ (x-3) = 1/3
ОДЗ: x-2>0
   x-3>0
log₈ $( \frac{x-2}{x-3} )$ = log₈2
$\frac{x-2}{x-3}=2$
x-2 = 2x - 6
-x = -4
x = 4
ответ: 4

1) lg (5-x) = 1/3 lg(35-x³)
ОДЗ: 5-x>0
   35-x³ > 0
lg (5-x) = lg $(35- x^{3}) ^{ \frac{1}{3} }$
5-x = $(35- x^{3}) ^{ \frac{1}{3} }$
(5-x)³ = 35-x³
125 - 3*25*x + 3*5*x² - x³ = 35-x³
125 - 75x + 15x² - 35 = 0
15x² - 75x +90 = 0
x² - 5x + 6 = 0
D = 25 - 24 = 1
x₁ = (5+1)/2 = 3
x₂ = (5-1) / 2 =2
ответ: 3; 2
2) log₂ $( \frac{x-5}{x+5} )$ + log₂ (x+5) = 0
ОДЗ: x-5>0
   x+5>0
log₂ $(\frac{(x-5)(x+5)}{x+5} )$ = 0
log₂ (x-5) = 0
x-5 = 1
x = 6
ответ: 6
3) log₂ (3x-6) - 1 = log₂ (9x-19)
log₂ (3x-6) = log₂ (9x-19) + 1
log₂ (3x-6) = log₂ (9x-19) + log₂2
log₂ (3x-6) = log₂ ((9x-19)*2)
3x-6 = 18x - 38
15x = 32
x = $\frac{32}{15}$
ответ: 32/15

1) log₇ (x-2) +log₇(x+2) = log₇ (4x+41)
ОДЗ: x-2>0
   x+2>0
   4x+41 >0
log₇ ((x-2)(x+2)) = log₇ (4x+41)
(x-2)(x+2) = 4x+41
x² - 4 = 4x +41
x² - 4x - 45 = 0
D₁ = 4 + 45 = 49
x₁ = 2+7 = 9
x₂ = 2-7 = -5 не удов. ОДЗ
ответ: 9
2) log₄ (x+1) - log₄(1-x) = log₄ (2x+3)
ОДЗ: x+1>0
   1-x>0
   2x+3>0
log₄ (x+1) = log₄(2x+3) + log₄ (1-x)
log₄ (x+1) = log₄ ((2x+3)(1-x))
x+1 = 2x - 2x² + 3 - 3x
2x² + 2x - 2 = 0
x² + x - 1 = 0
D = 1 + 4 = 5
x₁ = (-1+√5)/2
x₂ = (-1-√5) / 2 не удов.ОДЗ
ответ: (-1+√5) / 2
3) log₄ (x+3) - log₄ (x-1) = 2- log₄8
log₄ $(\frac{x+3}{x-1}) =$ log₄16 - log₄8
log₄ $( \frac{x+3}{x-1})$ = log₄2
( $\frac{x+3}{x-1}) = 2$
x+3 = 2x - 2
-x = -5
x = 5
ответ: 5
4) lg (x-1) + lg (x+1) = 3lg2 + lg (x-2)
lg ((x-1)(x+1)) = lg8 + lg (x-2)
lg (x² - 1) = lg (8(x-2))
x² - 1 = 8x- 16
x² - 8x + 15 = 0
D₁ = 16 - 15 = 1
x₁ = 4 + 1 =5
x₂ = 4-1 = 3
ответ: 5;3

1) 2log₃(x-2) + log₃ (x-4)² = 0
ОДЗ: x-2>0
   x-4>0
2log₃ (x-2)+ 2log₃ (x-4) = 0
2 (log₃(x-2) + log₃ (x-4)) = 0
log₃ ((x-2)(x-4)) = 0
(x-2)(x-4) = 1
x² - 4x - 2x + 8 = 1
x² - 6x + 7 = 0
D₁ = 9 - 7 = 2
x₁ = 3 + √2
x₂ = 3 -√2 не удов. ОДЗ
ответ; 3+√2
2) 2lgx - lg4 + lg (5-x²) = 0
ОДЗ: x>0
   5-x² > 0
lgx² + lg (5-x²) = lg4
lg (x² (5-x²)) = lg4
x² (5-x²) = 4
5x² - x⁴ = 4
5x² - x⁴ - 4 = 0
x⁴ - 5x² + 4 =0
x² = t ; t>0
t² - 5t + 4 = 0
t₁ = 1
t₂ = 4
x² = 1     x² = 4
x₁ = 1 x₁ = 2
x₂ = -1 x₂ = -2
корни -1 и -2 не удов. ОДЗ
ответ: 1; 2

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