Solve log_2 x + log_2 (x - 2) = 3 for x.
Answer and explanation
Correct answer: D. 4
- Step 1: Combine the logarithms: log_2 [x(x - 2)] = 3, so x(x - 2) = 2^3 = 8. Step 2. x^2 - 2 x - 8 = 0, which factorises as (x - 4)(x + 2) = 0. Step 3. The root x = -2 is rejected because it makes the logarithm undefined, so x = 4. Answer: 4. Why not the others: 2: That root makes x - 2 zero or negative, so the logarithm is not defined. 8: That is the value of the right-hand side, not of x. 6: That adds 2 where the factor is x - 2.
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