AQA C2 2007 January — Question 9

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2007
SessionJanuary
TopicLaws of Logarithms

9
  1. Solve the equation \(3 \log _ { a } x = \log _ { a } 8\).
  2. Show that $$3 \log _ { a } 6 - \log _ { a } 8 = \log _ { a } 27$$
    1. The point \(P ( 3 , p )\) lies on the curve \(y = 3 \log _ { 10 } x - \log _ { 10 } 8\). Show that \(p = \log _ { 10 } \left( \frac { 27 } { 8 } \right)\).
    2. The point \(Q ( 6 , q )\) also lies on the curve \(y = 3 \log _ { 10 } x - \log _ { 10 } 8\). Show that the gradient of the line \(P Q\) is \(\log _ { 10 } 2\).