Edexcel C12 2015 January — Question 6

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2015
SessionJanuary
TopicLaws of Logarithms

6. Given that $$2 \log _ { 4 } ( 2 x + 3 ) = 1 + \log _ { 4 } x + \log _ { 4 } ( 2 x - 1 ) , \quad x > \frac { 1 } { 2 }$$
  1. show that $$4 x ^ { 2 } - 16 x - 9 = 0$$
  2. Hence solve the equation $$2 \log _ { 4 } ( 2 x + 3 ) = 1 + \log _ { 4 } x + \log _ { 4 } ( 2 x - 1 ) , \quad x > \frac { 1 } { 2 }$$