Mathematics
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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 ln(x^2-lnx)-x^(1/x) <-1 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         ln ( x ^ 2 - ln x ) - x ^ ( 1 / x ) < -1         (1)
        From the definition field of ln
        x > 0        (2 )
        From the definition field of ln
         x ^ 2 - ln x > 0        (3 )
        From the definition field of divisor
        x ≠ 0        (4 )

    From inequality(1):
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!
    From inequality(2):
         x > 0
    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 < 0 或  x > 0

    From inequalities (1) and (2)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (5)
    From inequalities (3) and (5)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (6)
    From inequalities (4) and (6)
        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!    (7)

    The final solution set is :

        x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!




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