O-LevelAdditional MathematicsLogarithmic and exponential functions4037/22 · Oct/Nov 2010 · Q87 Marks
Solve the equation
- (i)lg(5x + 10) + 2lg3 = 1 + lg(4x + 12),[4]
- (ii)9²ʸ / 3⁷⁻ʸ = 3⁴ʸ⁺³ / 27ʸ⁻².[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.
- [B1] 2lg3 = lg9 or 2lg3 = lg3²
- [B1] 1 = lg10
- [M1] Use lg rules correctly to eliminate logs (e.g. 9(5x + 10) = 10(4x + 12))
- [A1] x = 6
- [M1] Express in powers of 3 (3⁴ʸ / 3⁷⁻ʸ = 3⁴ʸ⁺³ / 3³⁽ʸ⁻²⁾)
- [M1] Correctly use rules of indices
- [A1] y = 4
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