Сравните значения выражений a и b, если a=0, 1(6), b=√0, 2²-0, 12² (всё в квадратном корне)

2)

2x ≠ -1   ⇒ x ≠ -0.5

x -5 = 0  ⇒ x = 5

Метод интервалов

           +                            -                             +

(- 0,5) [5]

x ∈ (-0.5; 5]

х ≠ 7

х + 3 = 0   ⇒ х = -3

Метод интервалов

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[- 3] (7)

x ∈ (-∞; -3]∪ (7; +∞)

4)

-x² - 5x + 6 ≤ 0

-x² - 5x + 6 = 0

D = 25 +24 = 49 = 7²

x₁ = -0.5 · (5 - 7) = 1

x₂ = -0.5 · (5 + 7) = -6

Метод интервалов

         -                          +                           -

[- 6] [1]

x ∈ (-∞; -6] ∪ [1; + ∞)

3x² - 8x - 3 ≥ 0

3x² - 8x - 3 = 0

D = 64 +36 = 100 = 10²

x₁ =  (8 - 10) : 6 = -1/3

x₂ = (8 + 10) : 6 = 3

Метод интервалов

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[- 1/3] [3]

x ∈ (-∞; -1/3] ∪ [3; + ∞)

1) log₁₂3 + log₁₂4 = log₁₂(3*4) = log₁₂12 = 12) log₇98 - log₇2 = log₇(98/2) = log₇49 = 23) log₂5-log₂35 + log₂56 = log₂(5/35) + log₂56 = log₂(log₂8 = 34) log₁/₃5 - log₁/₃5 + log₁/₃ 9 = log₁/₃9 = -21) lg4 + lg250= lg(4*250) = lg1000 = 32) log₂6 - log₂ = log₂( = log₂32 = 53) (log₁₂4 + log₁₂36)² = (log₁₂144)² = 2² = 44) lg13 - lg 130 = lg = lg = -15) (log₂13-log₂52)⁵ = (log₂)⁵ = (log₂)⁵ = (-2)⁵ = -326) (log₀.₃9 - 2log₀.₃10)⁴ = (log₀.₃9 - log₀.₃100)⁴ = (log₀.₃)⁴ = (log₀.₃0.09)⁴ = 2⁴ = 161) log₃x = -1x = 3⁻¹ = 1/32) log₂x = -5x = 2⁻⁵ = 1/323) log₃x = 2x = 3² = 94) log₄x = 3x = 4³ = 645) log₄x = -3x = 4⁻³ = 1/646) log₇x = 0x = 7° = 17) log₁/₇x = 1x = 1/78) log₁/₂x = -3x = (1/2)⁻³ = 81) log₂log₂log₃81 = log₂log₂4 = log₂2 = 12) log₂log₃log₁/₃(1/27) = log₂log₃3 = log₂1 = 03) log₅125 = 3 = 24) log₄log₃81 = log₄4 = 1