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Assignment:Find the solution set of inequality lnx >log(2.718,x) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
ln x > log( 2.718 , x ) (1)
From the definition field of ln
x > 0 (2 )
From the definition field of log
2.718 > 0 (3 )
x > 0 并且 ≠ 1 (4 )
From inequality(1):
x < 1
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):
0 < x < 1 或 x > 1
From inequalities (1) and (2)
0 < x < 1 (5)
From inequalities (3) and (5)
0 < x < 1 (6)
From inequalities (4) and (6)
0 < x < 1 (7)
The final solution set is :
0 < x < 1 Your problem has not been solved here? Please take a look at the hot problems !