O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · Oct/Nov 2011 · Q35 Marks
Express logₓ 2 in terms of a logarithm to base 2.
- (i)Express logₓ 2 in terms of a logarithm to base 2.[1]
- (ii)Using the result of part (i), and the substitution u = log₂x, find the values of x which satisfy the equation log₂x² = 3 – 2 logₓ2.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.
- [B1] B1 for log2 2 / log2 x or 1 / log2 x
- [M1] M1 for a correct attempt to obtain and solve a quadratic equation in terms of u or log2 x
- [A1] A1 for u =1, 2
- [M1] M1 for attempt to solve an equation of the form logx = k leading to x = 2^k
- [A1] A1 for both
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