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Find the complete solution set of the inequality (log₁₀(x))² >= log₁₀(x) + 2. If the solution set is (0, a] union [b, infinity), find the value of the product a*b.
- 5
- 10
- 15
- 20
Correct answer: 10
Solution
Setting t = log₁₀(x) gives (t-2)(t+1) >= 0, so t <= -1 (x <= 1/10) or t >= 2 (x >= 100). Thus a=1/10, b=100, and a*b=10.
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