I've been reading through Stewart's Calculus textbook, and came across the following problem fairly early on -
What is $$\prod_{i = 2}^{31} \log_i (i + 1)\;?$$
I did some searching, and found that the answer is 5, but I have absolutely no idea how that was found. There may be something to do with induction that is used because of the context of the problem in the book, though I think that the solution may have more to do with the nature of logarithms themselves.
If anyone has any ideas/solutions, it would be most appreciated.
Hint
$$\log_i(i+1)=\frac{\ln (i+1)}{\ln (i) } \,.$$
Your product is the telescopic...