CAIE A-Level Mathematics 3.2.1 Logarithm Laws

CAIE A-Level Mathematics 3.2.1 Logarithm Laws
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise combining logarithms with product, quotient and power laws, removing them to solve exact or numerical equations and rejecting roots outside the original domain.

How this is tested

  • combine logarithmic sums, differences and coefficients into one valid logarithm
  • remove equal logarithms to form an algebraic equation and solve it to the stated accuracy
  • check every solution keeps each logarithm argument positive and reject invalid roots

Question 3

Question 3(a)

(a)

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

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Question 3(b)

(b)

Hence solve the equation log⁡3(4y+1)=1+2log⁡3(2y−1)\log _{3}(4 y+1)=1+2 \log _{3}(2 y-1), giving your answer correct to 2 decimal places.

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