O-LevelAdditional MathematicsLogarithmic and exponential functions4037/21 · May/June 2022 · Q26 Marks
Write 2lgx-(lg(x+6)+lg3) as a single logarithm to base 10.
- (a)Write 2lgx-(lg(x+6)+lg3) as a single logarithm to base 10.[2]
- (b)Hence solve the equation 2lgx-(lg(x+6) +lg3) = 0.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B2] lg(x²/(3(x+6))) oe, nfww
- [B1] for any two log laws applied correctly e.g. lg(x²/(x+6)) - lg3
- [B1] lg(x²/(3(x+6))) = lg1 or 10⁰ = x²/(3(x+6)) FT their lg(single logarithm) from part (a) providing a single logarithm
- [B1] x²-3x-18=0 dep on B2 in part (a)
- [M1] Factorises or solves their 3-term quadratic
- [A1] x = 6 indicated as only solution dep on B2 in part (a)
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