O-LevelAdditional MathematicsLogarithmic and exponential functions4037/22 · May/June 2015 · Q66 Marks

Solve 6ˣ⁻² = 1/4.

Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

[M1] (x-2) log 6 = log(1/4) oe or log₆(1/4) = x-2 oe or x log 6 = log(36) oe or x log 6 - log 36 = log 1 - log 4 oe
[A1] 1.23 or 1.226(29...) rot to 4 or more figures isw correct answer or 1.22 implies M1
Method 1 for (b):
[B3] logₐ (8x2y²x16y / 64y) = logₐ 4² oe or B2 if at most one error or omitted step or B1 if at most two errors or omitted steps
[B1] y = 2 not from wrong working
Method 2 for (b):
[B3,2,1,0] LHS terms logₐ2y² = logₐ2 + 2logₐy; logₐ8 = 3 logₐ2; logₐ16y = 4 logₐ2 + logₐy; -logₐ64y = -6 logₐ2 – logₐy; RHS term 2logₐ4 = 4logₐ2
[B1] y = 2 not from wrong working

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Topic: Logarithmic and exponential functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source: O-Level Additional Mathematics, May/June 2015 Paper 2 Variant 2, question 6.

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