Est. 1998 — 27 years of woodworking knowledge
Sunday Puzzler -- Logs
Alex Y
Sorry to have been MIA on the puzzler lately.
Determine the value of log2(3)*log3(4)*log4(5)*...*log127(128)
If there is any question of my intent, loga(b) is the log base a of b. I'm too lazy to try to find the way to enter subscripts for the "standard" notation. 
Re: Sunday Puzzler -- Logs
Larry Barrett
I had to dig out my high school text books, and now I think I know the answer to this one. Do you remember the story about Snow White?
I bet your next puzzle will require remembering how to use the A and B scales on a slide rule.
Correct!
Alex Y
Not a Dopey answer at all!
Re: Sunday Puzzler -- Logs
Larry Barrett
In case anyone is still interested in this one, it is necessary to recall that there are a few 'rules' about how to use logarithms, like the rule for multiplication which says that (using Alex's notation) loga(b*c) = loga(b) +loga(c).
The 'rule' that is needed to solve this puzzle is the rule about how to change the base: to change loga(b) from base a to base c, the rule says that loga(b) = logc(b)/logc(a).
So rewriting the problem, changing the base of each term to base 2 as we go along:
log2(3)*log3(4)*log4(5) * ... = log2(3)*(log2(4)/log2(3))*(log2(5)/log2(4))*... and see that numerators and denominators all cancel out except the last term, which in this problem is log2(128).
Re: Sunday Puzzler -- Logs
Kent B
Nah - I don't care. I'm still working on how the cat can get the duck
Re: Sunday Puzzler -- Logs
Alex Y
That's an improvement over the other solution I have seen--essentially the same, but expressing each log as a quotient of natural logs. That solution requires a conversion the other way at the end, but you avoided that by using log base 2.
Nice job!