Solve log_2 x + log_2 (x - 16) = 9 for x.
Answer and explanation
Correct answer: C. 32
- Step 1: Combine the logarithms: log_2 [x(x - 16)] = 9, so x(x - 16) = 2^9 = 512. Step 2. x^2 - 16 x - 512 = 0, which factorises as (x - 32)(x + 16) = 0. Step 3. The root x = -16 is rejected because it makes the logarithm undefined, so x = 32. Answer: 32. Why not the others: 16: That root makes x - 16 zero or negative, so the logarithm is not defined. 512: That is the value of the right-hand side, not of x. 48: That adds 16 where the factor is x - 16.
Practise more Exponential and logarithmic functions.
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