Question

Comparați numerele:
a) 14 < 2 la puterea n <129
b) 3 la puterea n + 1 <57 < 3 la puterea n + 1
c) 3 la puterea n + 1 <57 < 3 la puterea n + 2
d) 7 la puterea n - 2 <_ 343

va rog urgent! ​

Answer 1

Explicație:

a)

$14 < {2}^{n} < 129$

$14 < {2}^{n} => 3 < n$

=> n > 3

${2}^{n} < 129 => n < 7$

=> n < 7

3 < n < 7 => n ∈ (3; 7)

b)

${3}^{n + 1} < 57 < {3}^{n + 1}$

${3}^{n + 1} = {3}^{n + 1}$

=> n ∉ R

c)

${3}^{n + 1} < 57 < {3}^{n + 2}$

${3}^{n + 1} < 57 = > n + 1 < 4 = > n < 3$

$57 < {3}^{n + 2} = > 3 < n + 2 = > n > 1$

n ∈ (-∞; 3) ∪ (1; +∞) => n ∈cR

d)

${7}^{n - 2} < 343$

${7}^{3} = 343$

${7}^{n - 2} < {7}^{3} = > n - 2 < 3 = > n < 5$

=> n ∈ (-∞; 5)