O-LevelAdditional MathematicsLogarithmic and exponential functions4037/22 · Oct/Nov 2022 · Q45 Marks
Solve the equation log₃(11x-8) = 1 + 2/logₓ3 given that x > 1.
- Solve the equation log₃(11x-8) = 1 + 2/logₓ3 given that x > 1.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [M2] log₃(11x-8) = 1 + 2log₃x (M1 for correct use change of base in a correct equation so that all logs have consistent base: logₓ3 = log₃3/log₃x = 1/log₃x oe, soi OR logₓ(11x-8) = logₓ3 + 2 oe, soi)
- [A1] 3x² - 11x + 8 [= 0] oe, nfww
- [M1] Factorises their 3-term quadratic: (3x - 8)(x-1) [= 0] dep on at least M1 previously awarded
- [A1] x = 8/3 or 2.67 or 2.666[6...] rot to 3 or more dp as only solution
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