O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · Oct/Nov 2025 · Q57 Marks
Write 5lg a – 4lg b – 3 as a single base 10 logarithm.
- (a)Write 5lg a – 4lg b – 3 as a single base 10 logarithm.[3]
- (b)Solve the equation log₅(x+1) – logₓ₊₁(5) = 0.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [3] B2 for lg(a⁵ ÷ (1000b⁴)) or lg(a⁵/(10³b⁴))
- or B2 for lg (a⁵/b⁴ ÷ 1000)
- B1 for 3=lg1000 or lg10³ soi
- B1 for use of the power rule at least once
- [4] B1 For change of base seen in the equation, allow for log₅(x+1)- log₅(5)/log₅(x+1) = 0
- M1 For correct simplification to a 2-term quadratic and at least one solution, may be implied by a substitution
- A1 SC B1 if 'spotted' from a correct equation, x=4
- A1 A0 if rejected or crossed out, x = -4/5
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