SOLUTION: Find the exact value of (log base 2 of 3)(log base 3 of 4)(log base 4 of 5)...(log base n of n+1)(log base n+1 of 2) without using a calculator.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Find the exact value of (log base 2 of 3)(log base 3 of 4)(log base 4 of 5)...(log base n of n+1)(log base n+1 of 2) without using a calculator.       Log On


   

Question 946235: Find the exact value of (log base 2 of 3)(log base 3 of 4)(log base 4 of 5)...(log base n of n+1)(log base n+1 of 2) without using a calculator.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C%283%29%29=log%28%283%29%29%2Flog%28%282%29%29
log%283%2C%284%29%29=log%28%284%29%29%2Flog%28%283%29%29
log%284%2C%285%29%29=log%28%285%29%29%2Flog%28%284%29%29
log%285%2C%286%29%29=log%28%286%29%29%2Flog%28%285%29%29
log%28n%2C%28n%2B1%29%29=log%28%28n%2B1%29%29%2Flog%28%28n%29%29
log%28n%2B1%2C%282%29%29=log%28%282%29%29%2Flog%28%28n%2B1%29%29
Similarly for the rest of the terms.
Multiplying it all out would leave,
%281%2Flog%28%282%29%29%29%2Alog%28%282%29%29=highlight%281%29