A-LevelMathematicsLogarithmic and exponential functions9709/31 · May/June 2022 · Q14 Marks

Solve the equation 2(3^(2x−1)) = 4^(x+1), giving your answer correct to 2 decimal places.

Solve the equation 2(3^(2x−1)) = 4^(x+1), giving your answer correct to 2 decimal places.[4]

Mark scheme

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

[*M1] Use law of the logarithm of a product or a quotient or a power
[A1] Obtain a correct linear equation in any form e.g. In2+(2x-1)ln3=(x+1)In4 or log₂ 2 + (2x-1)log₂ 3 = (2x + 2) log₂ 2
[DM1] Solve for x Allow for unsimplified expression x = … Allow M1 M1 for x=1.45 from 6^(2x-1) = 4^(x+1).
[A1] Obtain answer x = 2.21 The question asks for 2 dp.
Alternative method for question 1
[M1 A1] Correct use of indices to obtain 2.25^x = 6 or 1.5^(2x) = 6
[M1] Correct use of logarithms to solve for x Allow solution of 2.25^x = 6 by trial and improvement as far as 2.2...
[A1] Obtain answer x = 2.21 Need to see an intermediate step / sequence of iterations.

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

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