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How many integral values of x satisfy the equation |log_(sqrt(3))(x - 2)| - |log₃(x - 2)| = 2?

1. 1
2. 2
3. 3
4. 4

Correct answer: 1

Solution

Setting t = log₃(x-2), the equation simplifies to |t| = 2, giving x = 11 (integer) and x = 2 + 1/9 (not integer), so there is exactly 1 integral solution.

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