Solve the logarithmic equation: log(x + 2) + log(x - 1) = 1 (where log is base 10).

Answer and explanation

Correct answer: B. x = 3

  1. Step 1: Apply product rule: log[(x + 2)(x - 1)] = 1.
  2. Step 2: Convert to exponential form: (x + 2)(x - 1) = 10^1 = 10.
  3. Step 3: Expand: x^2 + x - 2 = 10, so x^2 + x - 12 = 0.
  4. Step 4: Factor: (x + 4)(x - 3) = 0, giving x = -4 or x = 3.
  5. Step 5: Check domain: x > 1, so x = -4 is extraneous. Solution is x = 3.
Answer
x = 3.
Why not the others: 'x = -4' is an extraneous root where arguments are negative; 'x = 3 and x = -4' fails to reject the extraneous root; 'x = 8' adds 10 - 2.

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