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Solve the Ineqlity

Source: 2004 National High School Mathematics League, Exam One, Problem 3

March 17, 2020
inequalities

Problem Statement

The solution set to the inequality log⁡2x−1+12log⁡12x3+2>0\sqrt{\log_2 x-1}+\frac{1}{2}\log_{\frac{1}{2}}x^3+2>0 is (A)[2,3)(B)(2,3](C)[2,4)(D)(2,4]\text{(A)}[2,3)\qquad\text{(B)}(2,3]\qquad\text{(C)}[2,4)\qquad\text{(D)}(2,4]
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