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Assignment:Find the solution set of inequality log(1/2,(x+1)) <= -1 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
log( 1 / 2 , ( x + 1 ) ) <= -1 (1)
From the definition field of log
1 / 2 > 0 (2 )
( x + 1 ) > 0 also ≠ 1 (3 )
From inequality(1):
x ≤ -1 或 x ≥ 1
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):
-1 < x < 0 或 x > 0
From inequalities (1) and (2)
x ≤ -1 或 x ≥ 1 (4)
From inequalities (3) and (4)
x ≥ 1 (5)
The final solution set is :
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