CAIE P3 2014 June — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2014
SessionJune
TopicFactor & Remainder Theorem
TypeShow equation reduces to polynomial

6 It is given that \(2 \ln ( 4 x - 5 ) + \ln ( x + 1 ) = 3 \ln 3\).
  1. Show that \(16 x ^ { 3 } - 24 x ^ { 2 } - 15 x - 2 = 0\).
  2. By first using the factor theorem, factorise \(16 x ^ { 3 } - 24 x ^ { 2 } - 15 x - 2\) completely.
  3. Hence solve the equation \(2 \ln ( 4 x - 5 ) + \ln ( x + 1 ) = 3 \ln 3\).