Question 8 - A-Level Maths

Exam Board	AQA
Module	AS Paper 2 (AS Paper 2)
Year	2020
Session	June
Topic	Exponential Equations & Modelling

Using $y = 2 ^ { 2 x }$ as a substitution, show that $$16 ^ { x } - 2 ^ { ( 2 x + 3 ) } - 9 = 0$$ can be written as $$y ^ { 2 } - 8 y - 9 = 0$$ 8
Hence, show that the equation $$16 ^ { x } - 2 ^ { ( 2 x + 3 ) } - 9 = 0$$ has $x = \log _ { 2 } 3$ as its only solution.
Fully justify your answer.