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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality ln(x^2-lnx)-x^(1/x) <-1 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
ln ( x ^ 2 - ln x ) - x ^ ( 1 / x ) < -1 (1)
From the definition field of ln
x > 0 (2 )
From the definition field of ln
x ^ 2 - ln x > 0 (3 )
From the definition field of divisor
x ≠ 0 (4 )
From inequality(1):
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!
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 或 x > 0
From inequalities (1) and (2)
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range! (5)
From inequalities (3) and (5)
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range! (6)
From inequalities (4) and (6)
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range! (7)
The final solution set is :
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range!Your problem has not been solved here? Please take a look at the hot problems !