Solve the equation In(1-e-2x) + 3 = 0. Give your final answer correct to 4 decimal places.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.

1. [B1] State that 1 - e⁻²ˣ = e⁻³ OE, with In removed.
2. [M1] Use correct method to solve an equation of the form e±²ˣ = a, where a > 0, and a reasonable attempt at the B1, for ± 2xlne or ± xlne E.g. [e⁻²ˣ = 1 - e⁻³] -2x = ln(1 - e⁻³) OE. Can be numerical ln (1 – 0.049787) = ln 0.9502. Evidence of method must be seen.
3. [A1] Obtain answer 0.0255 CAO Must be 4 decimal places. No working seen scores 0.