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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 log(3,-x^2+72-6x)-log(3,5) <2 .
    Question type: Inequality
    Solution:
    The inequality can be reduced to 1 inequality:
         log( 3 , - x ^ 2 + 72 - 6 * x ) - log( 3 , 5 ) <2         (1)
        From the definition field of log
         3 > 0        (2 )
         - x ^ 2 + 72 - 6 * x > 0 also ≠ 1        (3 )

    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 ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
    From inequality(3):
         -12 < x < -11.944272 或  -11.944272 < x < 5.944272 或  5.944272 < x < 6

    From inequalities (1) and (2)
         x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!    (4)
    From inequalities (3) and (4)
         -12 < x < -11.944272 或  -11.944272 < x < 5.944272 或  5.944272 < x < 6     (5)

    The final solution set is :

         -12 < x < -11.944272 或  -11.944272 < x < 5.944272 或  5.944272 < x < 6




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