Edexcel P3 2023 June — Question 2

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2023
SessionJune
TopicLaws of Logarithms

2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bef290fb-fbac-4c9c-981e-5e323ac7182e-04_814_839_242_614} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows the linear relationship between \(\log _ { 6 } T\) and \(\log _ { 6 } x\)
The line passes through the points \(( 0,4 )\) and \(( 2,0 )\) as shown.
    1. Find an equation linking \(\log _ { 6 } T\) and \(\log _ { 6 } x\)
    2. Hence find the exact value of \(T\) when \(x = 216\)
  1. Find an equation, not involving logs, linking \(T\) with \(x\)