(Solved): a) Solve the following logarithmic simultaneous equations \( \log _{x} y=2 \quad \) and \( \quad y ...

a) Solve the following logarithmic simultaneous equations \( \log _{x} y=2 \quad \) and \( \quad y \log 4=x \log 8 \) [5 marks] b) The polynomial \( 2 x^{3}+a x^{2}+b x+1 \) is exactly divisible by \( 2 x-1 \) and \( x+1 \). Find the values of \( a \) and \( b \). Hence find the third factor of the expression. c) Solve for \( x \) and \( y \) where \( x \) and \( y \) are real numbers [5 marks] \[ \frac{x}{1+i}+\frac{y}{3+i}=4-2 i \]