\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
A geometric sequence is defined by its first term \(u_1=5\) and a common ratio \(r=3\).
Determine the index \(n\) for which the term \(u_n\) has a value of 3645.
\(n=\)