6х-(2х-(3х-(4х+4))) = 6х-(2х-(3х-4х-4)) = 6х-(2х-3х+4х+4) = 6х-2х+3х-4х-4 = 3х-4
sin^2 a + cos^2 a + sin^2 a = cos^2 a
sin^2 a + cos^2 a + sin^2 a - cos^2 a = 0
2sin^2 a = 0
sin a = 0
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
<span>lg(x-1)+lg(x+1)=lg(9x+9)</span>
ОДЗ: x-1>0 => x>1
x+1>0 => x>-1
9x+9>0 => 9x>-9 => x>-1
x>1
<span>lg(x-1)+lg(x+1)=(x-1)(x+1)=x^2-1^2=x^2-1</span>
lg(x^2-1)=lg(9x+9)
По свойству логарифма:
x^2-1=9x+9
x^2-9x-10=0
D=81+40=121
x(1)=9+11/2=10 (удовлетворяет ОДЗ)
x(2)=9-11/2=-2/2=-1 (не удовлетворяет ОДЗ)
Ответ: 10.