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Assignment:Find the solution set of inequality ln((sinx+lnx+e3)/cosx) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
ln ( ( sin x + ln x + e 3 ) / cos x ) >0 (1)
From the definition field of ln
x > 0 (2 )
From the definition field of ln
( sin x + ln x + e 3 ) / cos x > 0 (3 )
From inequality(1):
4.712389 < x < 10.995574 或 10.995574 < x < 17.27876 或 17.27876 < x < 23.561945 或 23.561945 < x < 29.84513 或 29.84513 < x < 36.128316 或 36.128316 < x < 42.411501 或 42.411501 < x < 48.694686 或 48.694686 < x < 54.977871 或 x > 54.977871
From inequality(2):
x > 0
From inequality(3):
0 < x < 1.570796 或 4.712389 < x < 7.853982 或 10.995574 < x < 14.137167 或 17.27876 < x < 20.420352 或 23.561945 < x < 26.703538
From inequalities (1) and (2)
4.712389 < x < 10.995574 或 10.995574 < x < 17.27876 或 17.27876 < x < 23.561945 或 23.561945 < x < 29.84513 或 29.84513 < x < 36.128316 或 36.128316 < x < 42.411501 或 42.411501 < x < 48.694686 或 48.694686 < x < 54.977871 或 x > 54.977871 (4)
From inequalities (3) and (4)
4.712389 < x < 7.853982 或 0 < x < 1.570796 或 10.995574 < x < 14.137167 或 或 17.27876 < x < 20.420352 或 4.712389 < x < 10.995574 或 23.561945 < x < 26.703538 (5)
The final solution set is :
4.712389 < x < 7.853982 或 0 < x < 1.570796 或 10.995574 < x < 14.137167 或 或 17.27876 < x < 20.420352 或 4.712389 < x < 10.995574 或 23.561945 < x < 26.703538 *Note: Radian.Your problem has not been solved here? Please take a look at the hot problems !