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

## Question

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