Exit fullscreen mode

Exponentials & Logarithms

Review question

Can we solve the equation $\log_2 x + \log_3 x = 1 + \log_4 x$?
Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8260

Printable/supporting materials Printable version Fullscreen mode Teacher notes

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.