CAIE P2 2013 June — Question 4

Exam BoardCAIE
ModuleP2 (Pure Mathematics 2)
Year2013
SessionJune
TopicExponential Equations & Modelling

4 The variables \(x\) and \(y\) satisfy the equation \(5 ^ { y + 1 } = 2 ^ { 3 x }\).
  1. By taking logarithms, show that the graph of \(y\) against \(x\) is a straight line.
  2. Find the exact value of the gradient of this line and state the coordinates of the point at which the line cuts the \(y\)-axis.