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           ☆1 inequalities

[ 1/1Inequality]
    Assignment:Find the solution set of inequality sqrt(log(2,x)) <3-log(2,x) .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality：
         sqrt ( log( 2 , x ) ) <3 - log( 2 , x )         (1)
        From the definition field of log
         2 > 0        (2 )
         x > 0 also ≠ 1        (3 )
        From the definition field of √
         log( 2 , x ) ≥ 0        (4 )
        From the definition field of log
         2 > 0        (5 )
         x > 0 并且 ≠ 1        (6 )

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    From inequality(1)：
         x < 3.242765
    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)：
         0 < x < 1 或  x ＞ 1
    From inequality(4)：
         x ≥ 1
    From inequality(5)：
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
    From inequality(6)：
         0 < x < 1 或  x ＞ 1

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    From inequalities (1) and (2)
         x < 3.242765    (7)
    From inequalities (3) and (7)
         0 < x < 1 或  1 < x < 3.242765     (8)
    From inequalities (4) and (8)
         1 < x < 3.242765     (9)
    From inequalities (5) and (9)
         1 < x < 3.242765     (10)
    From inequalities (6) and (10)
         1 < x < 3.242765     (11)

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    The final solution set is :
         1 < x < 3.242765

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