CAIE A-Level Mathematics 2.2.1 Logarithm Laws

CAIE A-Level Mathematics 2.2.1 Logarithm Laws
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise using product, quotient and power laws to combine logarithms, remove them and solve resulting algebraic equations while enforcing positive logarithm arguments.

How this is tested

  • combine log terms into one logarithm using the correct product, quotient or power law
  • equate positive arguments after removing equal logarithms and solve the resulting equation
  • reject any algebraic root that makes a logarithm argument zero or negative

Question 2(a)

[Maximum number: 3]

Show that the equation log4(2x+1)=2log4(3x1)2\log _{4}(2 x+1)=2 \log _{4}(3 x-1)-2 can be written as a quadratic equation in x.