Question

2 легких примера с ответами (нужно сделать с записями)

$lg(x+3)=-lg(3x+6)$

1) -2ul; 2) -2u-3; 3) -1; 4) -1ul

$(lg x)^{2}-lgx^{3} +2=0$

1) -10u10; 2) 100; 3) 1; 4) 10u100

Answer 1

lg = log(10)

lg(x + 3) = - lg(3x + 6)

одз

x + 3 > 0   x > -3

3x + 6 > 0   x > -2

x ∈ (-2, +∞)

lg(x + 3) =  lg 1/(3x + 6)

x + 3 = 1/(3x + 6)

3(x + 3)(x + 2) = 1

3(x² + 5x + 6) = 1

3x² + 15x + 17 = 0

D = 15² - 4*3*17 = 21

x₁₂ = ( -15 +- √21)/6

√21 ≈ 4.6

x₁ = (-15 - 4.6)/6 = - 19.6 / 6 < -2 нет

x₁ = (-15 + 4.6)/6 = - 10.4 / 6 > -2 да

ответ ( -15 + √21)/6

========

(lg x)² - lg x³ + 2 = 0

одз x > 0

lg x = y

(lg x)² - 3lg x + 2 = 0

lg x = y

y² - 3y + 2 = 0

y₁₂ = 1   2

y₁ = 1

lg x = 1

x = 10

y₂ = 2

lg x = 2

x = 100

ответ x = {10,100}