O-LevelAdditional MathematicsLogarithmic and exponential functions4037/22 · May/June 2010 · Q109 Marks
Given that logₚ X = 6 and logₚ Y = 4, find the value of
- (a)(i)logₚ (X²/Y).[2]
- (a)(ii)logᵧ X.[2]
- (b)Find the value of 2ᶻ, where z = 5 + log₂3.[3]
- (c)Express √512 as a power of 4.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- M1 for 2logₚ X - logₚ Y or logₚ (X²/Y)
- A1 for 8
- A1 for logₚ X / logₚ Y
- A1 for 1.5
- B1 for 2⁵ × 2^(log₂3) or log₂ 32 + log₂ 3
- M1 for 2⁵ × 3 or log₂ 96
- A1 for 96
- B1 for (√512) = 2^(9/2) or (512) = 4^(9/2) or x = log₄√512
- B1 for 4^(9/4)
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