Question

Determinati in fiecare cqz ,munerele naturale x,stiind ca :a) 2^2•x+1 mai mare sau egal cu 128
b)4^3•x-5>256

Answer 1

a) 4x+1 >/ 128

4x >/ 128-1

4x >/ 127

x >/ 127/4

x >/ 31,75  => x apartine [31,75, +infinit)

b) 64x -5 > 256

64x > 256+5

64x > 261

x> 261/64

x> 4,07

Answer 2

Răspuns:

Explicație pas cu pas:

a)

2²ˣ⁺¹ ≥ 128

128 = 2 x 64 = 2 x 8² = 2 x (2³)² = 2⁷

2²ˣ⁺¹ ≥  2⁷ =>  2 x + 1 ≥7 =>   2 x ≥ 7-1 =>  x ≥ 6 : 2 =>  x ≥3

⇒ x ∈ [ 3; + ∞)

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b)

4³ˣ⁻⁵ > 256

256 = 4 x 64 = 4 x 4³ = 4⁴

4³ˣ⁻⁵ > 4⁴ =>  3 x - 5 > 4 =>   3 x > 4 + 5 =>  x > 9 : 3 =>  x > 3

⇒   x ∈ ( 3; + ∞ )