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History of Inequality Computation > Answer
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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality 0
Question type: Inequality
Solution:
The inequality can be reduced to 8 inequalities：
0 < lg x (1)
lg x < ln x (2)
From the definition field of lg
x > 0 (3 )
ln x < sin x (4)
From the definition field of ln
x > 0 (5 )
sin x < cos x (6)
cos x < x (7)
x < x ^ 2 (8)
x ^ 2 < e x (9)
e x <10 ^ x (10)
From inequality(1)：
x ＞ 1
From inequality(2)：
x ＞ 1
From inequality(3)：
x ＞ 0
From inequality(4)：
x < 2.219107
From inequality(5)：
x ＞ 0
From inequality(6)：
-14.922565 < x < -11.780972 或 -8.63938 < x < -5.497787 或 -2.356194 < x < 0.785398 或 3.926991 < x < 7.068583 或 10.210176 < x < 13.351769
From inequality(7)：
x ＞ 0.739085
From inequality(8)：
x < 0 或 x ＞ 1
From inequality(9)：
x ＞ -0.703467
From inequality(10)：
x ＞ 0
From inequalities (1) and (2)
x ＞ 1 (11)
From inequalities (3) and (11)
x ＞ 1 (12)
From inequalities (4) and (12)
1 < x < 2.219107 (13)
From inequalities (5) and (13)
1 < x < 2.219107 (14)
From inequalities (6) and (14)
(15)
From inequalities (7) and (15)
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range! (16)
From inequalities (8) and (16)
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range! (17)
From inequalities (9) and (17)
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range! (18)
From inequalities (10) and (18)
x ∈ Φ (Φ is empty)that is, the inequality will never be estatlished within the real number range! (19)
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 ！
