SOLUTION: Evaluate log2(3) x log3(4) x log4(5) x log5(6) x log6(7) x log7(8)

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Question 791592: Evaluate log2(3) x log3(4) x log4(5) x log5(6) x log6(7) x log7(8)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate
Assume the problem is:
= ?
Not sure if there is an easier way to do this, but it can be done using the
change of base formula: log%28a%2C%28N%29%29 = log%28b%2C%28N%29%29%2Flog%28b%28a%29%29
:
A lot of math, so wrote a 10 line basic program that spit it out in milliseconds.
the quotient of these 6 expressions was exactly 3
Interesting that integer values occur:
the quotient of the 1st two = 2
the quotient of the given 6 = 3
the quotient of expressions up log%2815%2C%2816%29%29 = 4
the quotient of expressions up log%2831%2C%2832%29%29 = 5
the quotient of expressions up log%2863%2C%2864%29%29 = 6
the quotient of expressions up log%28127%2C%28128%29%29 = 7
:
Not sure how relevant this is to anything, but thought it was interesting. CK
Comments? email me at: ankor@att.net