OCR C3 2006 June — Question 4

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Year2006
SessionJune
TopicExponential Equations & Modelling

4 It is given that \(y = 5 ^ { x - 1 }\).
  1. Show that \(x = 1 + \frac { \ln y } { \ln 5 }\).
  2. Find an expression for \(\frac { \mathrm { d } x } { \mathrm {~d} y }\) in terms of \(y\).
  3. Hence find the exact value of the gradient of the curve \(y = 5 ^ { x - 1 }\) at the point (3, 25).