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☆1 inequalities
[ 1/1Inequality]
Assignment:Find the solution set of inequality log(lnx,lgx) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
log( ln x , lg x ) >0 (1)
From the definition field of ln
x > 0 (2 )
From the definition field of lg
x > 0 (3 )
From the definition field of log
ln x > 0 (4 )
lg x > 0 also ≠ 1 (5 )
From inequality(1):
1 < x < 2.718282 或 x > 10
From inequality(2):
x > 0
From inequality(3):
x > 0
From inequality(4):
x > 1
From inequality(5):
1 < x < 10 或 x > 10
From inequalities (1) and (2)
1 < x < 2.718282 或 x > 10 (6)
From inequalities (3) and (6)
1 < x < 2.718282 或 x > 10 (7)
From inequalities (4) and (7)
1 < x < 2.718282 或 x > 10 (8)
From inequalities (5) and (8)
1 < x < 2.718282 或 x > 10 (9)
The final solution set is :
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