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Assignment:Find the solution set of inequality (ln(1+1/100^x))-(1+100^x)^(1/x)+100 <0 .
Question type: Inequality
Solution:
The inequality can be reduced to 1 inequality:
( ln ( 1 + 1 / 100 ^ x ) ) - ( 1 + 100 ^ x ) ^ ( 1 / x ) + 100 <0 (1)
From the definition field of ln
1 + 1 / 100 ^ x > 0 (2 )
From the definition field of divisor
x ≠ 0 (3 )
From inequality(1):
0 < x < 4.723516 或 4.723516 < x < 4.98233 或 4.98233 < x < 5.260431 或 5.260431 < x < 5.574204 或 5.574204 < x < 60359/9900 或 x > 60359/9900
From inequality(2):
x ∈ R (R is all real numbers),that is, in the real number range, the inequality is always established!
From inequality(3):
x < 0 或 x > 0
From inequalities (1) and (2)
0 < x < 4.723516 或 4.723516 < x < 4.98233 或 4.98233 < x < 5.260431 或 5.260431 < x < 5.574204 或 5.574204 < x < 60359/9900 或 x > 60359/9900 (4)
From inequalities (3) and (4)
0 < x < 4.723516 或 4.723516 < x < 4.98233 或 4.98233 < x < 5.260431 或 5.260431 < x < 5.574204 或 5.574204 < x < 60359/9900 或 x > 60359/9900 (5)
The final solution set is :
0 < x < 4.723516 或 4.723516 < x < 4.98233 或 4.98233 < x < 5.260431 或 5.260431 < x < 5.574204 或 5.574204 < x < 60359/9900 或 x > 60359/9900Your problem has not been solved here? Please take a look at the hot problems !