O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · Oct/Nov 2016 · Q36 Marks
By using the substitution y = log₃x, or otherwise, find the values of x for which 3 (log₃x)² + log₃x⁵ – log₃9 = 0.
- By using the substitution y = log₃x, or otherwise, find the values of x for which 3 (log₃x)² + log₃x⁵ – log₃9 = 0.[6]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.
- [1] (Equation in y): 3y² + 5y - 2 = 0
- [1] (Equivalent log form): 5log₃x and -2
- [1] y = 1/3, y = -2 M1 for correct attempt at the solution of their quadratic equation
- [1] x = 3^(1/3), x = 3⁻² M1 for dealing with one base 3 logarithm correctly
- [1] x = 1.44 (A1)
- [1] x = 1/9 (A1)
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