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(1+1/100^x))-(1+100^x)^(1/x)+100 <0 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         ( ln ( 1 + 1 / 100 ^ x ) ) - ( 1 + 100 ^ x ) ^ ( 1 / x ) + 100 <0         (1)
        From the definition field of ln
         1 + 1 / 100 ^ x > 0        (2 )
        From the definition field of divisor
        x ≠ 0        (3 )

    From inequality(1):
         0 < x < 4.723516 或  4.723516 < x < 4.98233 或  4.98233 < x < 5.260431 或  5.260431 < x < 5.574204 或  5.574204 < x < 60359/9900 或  x > 60359/9900
    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 < 0 或  x > 0

    From inequalities (1) and (2)
         0 < x < 4.723516 或  4.723516 < x < 4.98233 或  4.98233 < x < 5.260431 或  5.260431 < x < 5.574204 或  5.574204 < x < 60359/9900 或  x > 60359/9900    (4)
    From inequalities (3) and (4)
         0 < x < 4.723516 或  4.723516 < x < 4.98233 或  4.98233 < x < 5.260431 或  5.260431 < x < 5.574204 或  5.574204 < x < 60359/9900 或  x > 60359/9900    (5)

    The final solution set is :

         0 < x < 4.723516 或  4.723516 < x < 4.98233 或  4.98233 < x < 5.260431 或  5.260431 < x < 5.574204 或  5.574204 < x < 60359/9900 或  x > 60359/9900




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