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current location:Mathematical operation > History of Inequality Computation > Answer
    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




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