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