91Ó°ÊÓ

In the expansion of \((a-2 b)^{3}\) the coefficient of \(b^{2}\) is: (a) \(-2 a^{2}\) (b) \(-8 a\) (c) \(12 a\) (d) \(-4 a\) (e) \(-12\).

Solve the simultaneous equations \(\log (x-2)+\log 2=2 \log y\) \(\log (x-3 y+3)=0\).

Show that \(\log _{16}(x y)=\frac{1}{2} \log _{4} x+\frac{1}{2} \log _{4} y .\) Hence, or otherwise, solve the simultaneous equations $$ \begin{aligned} &\log _{16}(x y)=3 \frac{1}{2} \\ &\frac{\left(\log _{4} x\right)}{\left(\log _{4} y\right)}=-8 \end{aligned} $$

Without using tables, solve each of the following equations for \(x\), expressing your answers as simply as possible: (a) \(9 \log _{x} 5=\log _{5} x\), (b) \(\log _{8} \frac{x}{2}=\frac{\log _{8} x}{\log _{8} 2}\).