Solve log_2 x + log_2 (x - 8) = 7 for x.
Answer and explanation
Correct answer: D. 16
- Step 1: Combine the logarithms: log_2 [x(x - 8)] = 7, so x(x - 8) = 2^7 = 128. Step 2. x^2 - 8 x - 128 = 0, which factorises as (x - 16)(x + 8) = 0. Step 3. The root x = -8 is rejected because it makes the logarithm undefined, so x = 16. Answer: 16. Why not the others: 8: That root makes x - 8 zero or negative, so the logarithm is not defined. 128: That is the value of the right-hand side, not of x. 24: That adds 8 where the factor is x - 8.
Practise more Exponential and logarithmic functions.
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