A-LevelMathematicsLogarithmic and exponential functions9709/32 · May/June 2022 · Q14 Marks

Solve the equation ln(e2x + 3) = 2x + ln 3, giving your answer correct to 3 decimal places.

(a)Solve the equation ln(e2x + 3) = 2x + ln 3, giving your answer correct to 3 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, power or quotient or a law of indices (on an expression that is relevant to the question) e.g. ln(e2x + 3) - ln3 = ln (e2x + 3)/3 or e(2x+ln3) = e2xeln3
A1 State a correct equation without logs (in any form) e.g. 3+ e2x = 3e2x
M1 Carry out correct method to solve an equation of the form e2x = a, where a > 0, or for solving ex = b (b > 0) if they have already taken the square root M1 Allow for x = ½ ln3. M1 can be implied by correct answer.
A1 Obtain answer x = 0.203 CAO. The question requires 3 d.p. Answer only with no working shown is 0/4.

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Topic: Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2022 Paper 3 Variant 2, question 1.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content