If 60^a = 3 and 60^b = 5

 
 
60-a-b-1

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Number Puzzles and tagged . Bookmark the permalink.

2 Responses to If 60^a = 3 and 60^b = 5

  1. Paul says:

    The answer is

    2

    P

    • benvitalis says:

      That’s right.

      60^a = 3
      60^b = 5
      means:
      a = (log(3))/(2 log(2) + log(3) + log(5))
      b = (log(5))/(2 log(2) + log(3) + log(5))

      Now, 12^((1-a-b)/(2(1-b)))

      2(1-b)
      = 2(1-(log(5))/(2 log(2) + log(3) + log(5)))
      = (log(144))/(log(60))

      1-a-b
      = 1-(log(3))/(2 log(2) + log(3) + log(5))-(log(5))/(2 log(2) + log(3) + log(5))
      = (log(4))/(log(60))

      ((log(4))/(log(60)))/((log(144))/(log(60))) = (log(2))/(log(12))

      12^((log(2))/(log(12))) = 2

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