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Assignment:Find the solution set of inequality log(0.5,x^2+2x-3)
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
log( 0.5 , x ^ 2 + 2 * x - 3 ) < log( 0.5 , 3 * x + 3 ) (1)
From the definition field of log
0.5 > 0 (2 )
x ^ 2 + 2 * x - 3 > 0 also ≠ 1 (3 )
From the definition field of log
0.5 > 0 (4 )
3 * x + 3 > 0 并且 ≠ 1 (5 )
From inequality(1):
x < 1 或 x > 3
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 < -3.236068 或 -3.236068 < x < -3 或 1 < x < 1.236068 或 x > 1.236068
From inequality(4):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(5):
-1 < x < -2/3 或 x > -2/3
From inequalities (1) and (2)
x < 1 或 x > 3 (6)
From inequalities (3) and (6)
x < -3.236068 或 -3.236068 < x < -3 或 x > 3 (7)
From inequalities (4) and (7)
x < -3.236068 或 -3.236068 < x < -3 或 x > 3 (8)
From inequalities (5) and (8)
x > 3 或 x > 3 (9)
The final solution set is :
x > 3 或 x > 3Your problem has not been solved here? Please take a look at the hot problems !