Overview: 1 questions will be solved this time.Among them
           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality e^{((lnx)/x^(1/2))+((lnx)/(x^(1/8)))}*e^((lnx/(x^(1/8))))+e^((lnx)/(x^(1/2))) >2e^((lnx/(x^(1/8)))) .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality：
         e ^ ( ( ( ln x ) / x ^ ( 1 / 2 ) ) + ( ( ln x ) / ( x ^ ( 1 / 8 ) ) ) ) * e ^ ( ( ln x / ( x ^ ( 1 / 8 ) ) ) ) + e ^ ( ( ln x ) / ( x ^ ( 1 / 2 ) ) ) >2 * e ^ ( ( ln x / ( x ^ ( 1 / 8 ) ) ) )         (1)
        From the definition field of ln
        x > 0        (2 )
        From the definition field of divisor
        x ≠ 0        (3 )
        From the definition field of ln
        x > 0        (4 )
        From the definition field of divisor
         x ^ ( 1 / 8 ) ≠ 0        (5 )
        From the definition field of ln
        x > 0        (6 )
        From the definition field of divisor
         x ^ ( 1 / 8 ) ≠ 0        (7 )
        From the definition field of ln
        x > 0        (8 )
        From the definition field of divisor
         x ^ ( 1 / 2 ) ≠ 0        (9 )
        From the definition field of ln
        x > 0        (10 )
        From the definition field of divisor
         x ^ ( 1 / 8 ) ≠ 0        (11 )

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    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 ＞ 0
    From inequality(3)：
         x < 0 或  x ＞ 0
    From inequality(4)：
         x ＞ 0
    From inequality(5)：
         x ∈ R （R为全体实数），即在实数范围内，不等式恒成立！
    From inequality(6)：
         x ＞ 0
    From inequality(7)：
         x ∈ R （R为全体实数），即在实数范围内，不等式恒成立！
    From inequality(8)：
         x ＞ 0
    From inequality(9)：
         x ∈ R （R为全体实数），即在实数范围内，不等式恒成立！
    From inequality(10)：
         x ＞ 0
    From inequality(11)：
         x ∈ R （R为全体实数），即在实数范围内，不等式恒成立！

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    From inequalities (1) and (2)
         x ＞ 0    (12)
    From inequalities (3) and (12)
         x ＞ 0    (13)
    From inequalities (4) and (13)
         x ＞ 0    (14)
    From inequalities (5) and (14)
         x ＞ 0    (15)
    From inequalities (6) and (15)
         x ＞ 0    (16)
    From inequalities (7) and (16)
         x ＞ 0    (17)
    From inequalities (8) and (17)
         x ＞ 0    (18)
    From inequalities (9) and (18)
         x ＞ 0    (19)
    From inequalities (10) and (19)
         x ＞ 0    (20)
    From inequalities (11) and (20)
         x ＞ 0    (21)

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    The final solution set is :
         x ＞ 0

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