CAIE P2 2007 June — Question 2

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2007
SessionJune
TopicExponential Equations & Modelling

2 The variables \(x\) and \(y\) satisfy the relation \(3 ^ { y } = 4 ^ { x + 2 }\).
  1. By taking logarithms, show that the graph of \(y\) against \(x\) is a straight line. Find the exact value of the gradient of this line.
  2. Calculate the \(x\)-coordinate of the point of intersection of this line with the line \(y = 2 x\), giving your answer correct to 2 decimal places.