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O-LevelAdditional MathematicsLogarithmic and exponential functions4037/21 · May/June 2012 · Q56 Marks

Solve the equation 3²ˣ = 1000, giving your answer to 2 decimal places.

(a)Solve the equation 3²ˣ = 1000, giving your answer to 2 decimal places.[2]
(b)Solve the equation 36^(2y-5) / 6^(3y) = 6^(2y-1) / 216^(y+6).[4]

Mark scheme

Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.

[1] (a) 2x log 3 = log 1000 M1
[1] 3.14 cao A1
[1] (b) Express in powers of 6 M1
[1] 6^(4y-10) / 6^(3y) = 6^(2y-1) / 6^(3y+18) A1
[1] Uses rules of indices (4y-10-3y = 2y-1-3y-18) M1
[1] y = -4.5 A1

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About this question

Topic: Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source: O-Level Additional Mathematics, May/June 2012 Paper 2 Variant 1, question 5.

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