CAIE A-Level Mathematics 2.2.3 Log equations

CAIE A-Level Mathematics 2.2.3 Log equations
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise solving equations and inequalities where the unknown is in an index, using logarithms and substitutions such as e^x.

How this is tested

  • take logs of both sides and apply the power law to make x appear outside indices
  • solve quadratic forms in e^x or e^{2x}, rejecting impossible negative exponential values

Question 2

[Maximum number: 3]

Solve the equation e2x(e2x−8)=48\mathrm{e}^{2 x}\left(\mathrm{e}^{2 x}-8\right)=48 ．