Edexcel C2 2013 June — Question 6

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2013
SessionJune
TopicLaws of Logarithms

6. Given that \(\log _ { 3 } x = a\), find in terms of \(a\),
  1. \(\log _ { 3 } ( 9 x )\)
  2. \(\log _ { 3 } \left( \frac { x ^ { 5 } } { 81 } \right)\)
    giving each answer in its simplest form.
  3. Solve, for \(x\), $$\log _ { 3 } ( 9 x ) + \log _ { 3 } \left( \frac { x ^ { 5 } } { 81 } \right) = 3$$ giving your answer to 4 significant figures. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{4f4eac7b-8908-480f-bb39-049944203fff-10_775_1605_221_159} \captionsetup{labelformat=empty} \caption{Figure 1}
    \end{figure} The line with equation \(y = 10\) cuts the curve with equation \(y = x ^ { 2 } + 2 x + 2\) at the points \(A\) and \(B\) as shown in Figure 1. The figure is not drawn to scale.