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a KISS puzzle (Posted on 2017-02-27) Difficulty: 2 of 5
Prove:

logpie + logepi >2

Looks complicated?
It is not!

See The Solution Submitted by Ady TZIDON    
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Solution | Comment 1 of 2
logpi+ logepi =  logee / logepi logepi  [change to common base e]
                         
                      = 1/ln pi  + ln pi .   [usual notation for natural logs]
                      = 1/L + L   , say
Now 1/L + L > 2 iff  L^2 - 2L + 1 > 0   and L > 0 
                         iff (L - 1)^2 > 0 and  L > 0 .........  Eq. 1
     Now L = ln pi  >  1 since  pi > e
     Therefore, Eq. 1 is true and the result is proved.

Nice problem, Ady!

Edited on February 27, 2017, 9:58 am
  Posted by JayDeeKay on 2017-02-27 09:52:04

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