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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality lnx >log(x,lnx) .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
ln x > log( x , ln x ) (1)
From the definition field of ln
x > 0 (2 )
From the definition field of ln
x > 0 (3 )
From the definition field of log
x > 0 (4 )
ln x > 0 并且 ≠ 1 (5 )
From inequality(1):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(2):
x > 0
From inequality(3):
x > 0
From inequality(4):
x > 0
From inequality(5):
1 < x < 2.718282 或 x > 2.718282
From inequalities (1) and (2)
x > 0 (6)
From inequalities (3) and (6)
x > 0 (7)
From inequalities (4) and (7)
x > 0 (8)
From inequalities (5) and (8)
1 < x < 2.718282 或 x > 2.718282 (9)
The final solution set is :
1 < x < 2.718282 或 x > 2.718282Your problem has not been solved here? Please take a look at the hot problems !