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Assignment:Find the solution set of inequality ln((sin1/x+lgx+e3)/cosx) >0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality：
ln ( ( sin 1 / x + lg x + e 3 ) / cos x ) >0 (1)
From the definition field of divisor
x ≠ 0 (2 )
From the definition field of lg
x > 0 (3 )
From the definition field of ln
( sin 1 / x + lg x + e 3 ) / cos x > 0 (4 )
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 或 x ＞ 0
From inequality(3)：
x ＞ 0
From inequality(4)：
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 (5)
From inequalities (3) and (5)
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 (6)
From inequalities (4) and (6)
4.712389 < x < 7.853982 或 x ＞ 54.977871 或 10.995574 < x < 14.137167 或 x < -2 或 17.27876 < x < 20.420352 或 10.995574 < x < 17.27876 或 23.561945 < x < 26.703538 (7)
The final solution set is :
4.712389 < x < 7.853982 或 x ＞ 54.977871 或 10.995574 < x < 14.137167 或 x < -2 或 17.27876 < x < 20.420352 或 10.995574 < x < 17.27876 或 23.561945 < x < 26.703538 *Note: Radian.Your problem has not been solved here? Please take a look at the hot problems ！
