Solve log_3 x + log_3 (x - 6) = 3 for x.
Answer and explanation
Correct answer: D. 9
- Step 1: Combine the logarithms: log_3 [x(x - 6)] = 3, so x(x - 6) = 3^3 = 27. Step 2. x^2 - 6 x - 27 = 0, which factorises as (x - 9)(x + 3) = 0. Step 3. The root x = -3 is rejected because it makes the logarithm undefined, so x = 9. Answer: 9. Why not the others: 3: That root makes x - 6 zero or negative, so the logarithm is not defined. 27: That is the value of the right-hand side, not of x. 15: That adds 6 where the factor is x - 6.
Practise more Exponential and logarithmic functions.
Free questions with an explanation for every one, and full timed CSAT Suneung mock tests.