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A-LevelMathematicsLogarithmic and exponential functions9709/33 · Oct/Nov 2022 · Q14 Marks

Solve the equation ln(2x – 1) = 2ln(x + 1) – lnx. Give your answer correct to 3 decimal places.

Solve the equation ln(2x – 1) = 2ln(x + 1) – lnx. Give your answer correct to 3 decimal places.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

M1 Use law for the logarithm of a product, quotient or power
A1 Remove logarithms and state a correct equation, e.g. x(2x−1)=(x+1)²
M1 Solve a 3-term quadratic obtaining at least one root
A1 Obtain answer 3.303 only

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About this question

Topic: Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, Oct/Nov 2022 Paper 3 Variant 3, question 1.

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