Log₃ (x² - 4x + 4) = 2
x² - 4x + 4 = 9
x² - 4x - 5 = 0
По теореме Виета:
x₁ = -1
x₂ = 5
3log₄ x = log₄ 12,5 + log₄ 64
log₄ x³ = log₄ 800
x³ = 800
x = 2
2log₃ (x-2) - log₃ (x+1) = 1
log₃ (x-2)² - log₃ (x+1) = 1
log₃ (x-2)² = log₃ 3 + log₃ (x+1)
log₃ (x-2)² = log₃ 3(x+1)
x² - 4x + 4 = 3x + 3
x² - 7x + 1 = 0
D = (-7)² - 4 = 45
x₁ =
x₂ =
<span>log₄ (x-4) + log₄ (x+4) = log₄ (3x+2)
</span>log₄ (x-4)(x+4) = log₄ (3x+2)
x² - 16 = 3x+2
x² - 3x - 18 = 0
По теореме Виета:
x₁ = -3
x₂ = 6
I)
x^3-2x^2-9x+18=0
x*(x^2-9)-2*(x^2-9)=0
(x-2)(x^2-9)=0
(x-2)(x-3)(x+3)=0
x=2,±3
II)
(P1) 8х-2у=7
(P2) 8х-4у=3
(P1 - P2) 8x-2y-8x-(-4y)=7-3
2y=4
y=2
(P1 y=2) 8x-2*2=7
x=11/8
x>0
y>0
Первая четверть
III)
6/x-5+x=0
x=3
x=2
x^3-5x^2/2+6x=0.1