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           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality lgx >lnx     Question type: Inequality
    Solution:
    The inequality can be reduced to 2 inequalities：
         lg x > ln x         (1)
        From the definition field of lg
        x > 0        (2 )
         ln x < x         (3)
        From the definition field of ln
        x > 0        (4 )

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    From inequality(1)：
         x < 1
    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

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    From inequalities (1) and (2)
         0 < x < 1     (5)
    From inequalities (3) and (5)
         0 < x < 1     (6)
    From inequalities (4) and (6)
         0 < x < 1     (7)

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    The final solution set is :
         0 < x < 1

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