## Question

- If \(a\), \(b\), \(c\) are positive and are the \(p\)th, \(q\)th, \(r\)th terms of a geometric progression prove that
\[\begin{equation*}
(q-r) \log a + (r-p) \log b + (p-q) \log c = 0.
\end{equation*}\]
- Solve the equation \(\log_2 x + \log_3 x = 1 + \log_4 x\), giving your answer to three significant figures.