Solve log_5 x + log_5 (x - 20) = 3 for x.
Answer and explanation
Correct answer: D. 25
- Step 1: Combine the logarithms: log_5 [x(x - 20)] = 3, so x(x - 20) = 5^3 = 125. Step 2. x^2 - 20 x - 125 = 0, which factorises as (x - 25)(x + 5) = 0. Step 3. The root x = -5 is rejected because it makes the logarithm undefined, so x = 25. Answer: 25. Why not the others: 5: That root makes x - 20 zero or negative, so the logarithm is not defined. 125: That is the value of the right-hand side, not of x. 45: That adds 20 where the factor is x - 20.
Practise more Exponential and logarithmic functions.
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