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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.

1. 5
2. 10
3. 15
4. 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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