- In this question you must show detailed reasoning.
Solutions relying entirely on calculator technology are not acceptable.
- Given that
$$2 \log _ { 4 } ( x + 3 ) + \log _ { 4 } x = \log _ { 4 } ( 4 x + 2 ) + \frac { 1 } { 2 }$$
show that
$$x ^ { 3 } + 6 x ^ { 2 } + x - 4 = 0$$
- Given also that - 1 is a root of the equation
$$x ^ { 3 } + 6 x ^ { 2 } + x - 4 = 0$$
solve
$$2 \log _ { 4 } ( x + 3 ) + \log _ { 4 } x = \log _ { 4 } ( 4 x + 2 ) + \frac { 1 } { 2 }$$
\section*{(Total for Question 10 is 6 marks)}