CAIE P3 2020 November — Question 3

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2020
SessionNovember
TopicExponential Equations & Modelling

3 The variables \(x\) and \(y\) satisfy the relation \(2 ^ { y } = 3 ^ { 1 - 2 x }\).
  1. By taking logarithms, show that the graph of \(y\) against \(x\) is a straight line. State the exact value of the gradient of this line.
  2. Find the exact \(x\)-coordinate of the point of intersection of this line with the line \(y = 3 x\). Give your answer in the form \(\frac { \ln a } { \ln b }\), where \(a\) and \(b\) are integers.