Edexcel IALGeneralGeneral Applications6 Marks
Solve the equation 2 log₃(x) - log₃(x + 6) = 1.
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- M1 for using the power rule for logarithms: log₃(x²) or 2 log₃(x).
- M1 for using the subtraction rule for logarithms: log₃(x² / (x + 6)).
- A1 for correctly forming log₃(x² / (x + 6)) = 1.
- M1 for converting to index form: x² / (x + 6) = 3¹ or x² = 3(x + 6).
- A1 for forming a correct 3-term quadratic equation: x² - 3x - 18 = 0.
- A1 for correct solution x = 6 only (rejecting x = -3 as log₃(-3) is undefined).
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