Explicație:
a)
[tex]14 < {2}^{n} < 129[/tex]
[tex]14 < {2}^{n} => 3 < n[/tex]
=> n > 3
[tex]{2}^{n} < 129 => n < 7[/tex]
=> n < 7
3 < n < 7 => n ∈ (3; 7)
b)
[tex]{3}^{n + 1} < 57 < {3}^{n + 1} [/tex]
[tex]{3}^{n + 1} = {3}^{n + 1}[/tex]
=> n ∉ R
c)
[tex]{3}^{n + 1} < 57 < {3}^{n + 2} [/tex]
[tex]{3}^{n + 1} < 57 = > n + 1 < 4 = > n < 3[/tex]
[tex]57 < {3}^{n + 2} = > 3 < n + 2 = > n > 1[/tex]
n ∈ (-∞; 3) ∪ (1; +∞) => n ∈cR
d)
[tex]{7}^{n - 2} < 343[/tex]
[tex]{7}^{3} = 343[/tex]
[tex]{7}^{n - 2} < {7}^{3} = > n - 2 < 3 = > n < 5[/tex]
=> n ∈ (-∞; 5)
