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Assignment:Find the solution set of inequality sqrt(n) >= log(2,2n) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
sqrt ( n ) >= log( 2 , 2 * n ) (1)
From the definition field of √
x ≥ 0 (2 )
From the definition field of log
2 > 0 (3 )
2 * x > 0 并且 ≠ 1 (4 )
From inequality(1):
n ≤ 1 或 n ≥ 39.938891
From inequality(2):
n ≥ 0
From inequality(3):
n ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(4):
0 < n < 1/2 或 n > 1/2
From inequalities (1) and (2)
0 ≤ n ≤ 1 或 n ≥ 39.938891 (5)
From inequalities (3) and (5)
0 ≤ n ≤ 1 或 n ≥ 39.938891 (6)
From inequalities (4) and (6)
0 < n < 1/2 或 1/2 < n ≤ 1 或 n ≥ 39.938891 (7)
The final solution set is :
0 < n < 1/2 或 1/2 < n ≤ 1 或 n ≥ 39.938891Your problem has not been solved here? Please take a look at the hot problems !