Solve log_2 x + log_2 (x - 4) = 5 for x.
Answer and explanation
Correct answer: B. 8
- Step 1: Combine the logarithms: log_2 [x(x - 4)] = 5, so x(x - 4) = 2^5 = 32. Step 2. x^2 - 4 x - 32 = 0, which factorises as (x - 8)(x + 4) = 0. Step 3. The root x = -4 is rejected because it makes the logarithm undefined, so x = 8. Answer: 8. Why not the others: 4: That root makes x - 4 zero or negative, so the logarithm is not defined. 32: That is the value of the right-hand side, not of x. 12: That adds 4 where the factor is x - 4.
Practise more Exponential and logarithmic functions.
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