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Overview: 1 questions will be solved this time.Among them
☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality log(2,abs(z)+√(z^2+1)) <1 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
log( 2 , abs ( z ) + √ ( z ^ 2 + 1 ) ) <1 (1)
From the definition field of √
x ^ 2 + 1 ≥ 0 (2 )
From the definition field of log
2 > 0 (3 )
abs ( x ) + √ ( x ^ 2 + 1 ) > 0 also ≠ 1 (4 )
From inequality(1):
-3/4 < z < 3/4
From inequality(2):
z ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(3):
z ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(4):
z < 0 或 z > 0
From inequalities (1) and (2)
-3/4 < z < 3/4 (5)
From inequalities (3) and (5)
-3/4 < z < 3/4 (6)
From inequalities (4) and (6)
-3/4 < z < 0 或 0 < z < 3/4 (7)
The final solution set is :
-3/4 < z < 0 或 0 < z < 3/4 Your problem has not been solved here? Please take a look at the hot problems !