Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Prove that: e^pi > pi^e, without using a calculator

  1. Sep 24, 2004 #1
    How can you prove that:
    e^pi > pi^e,
    without using a calculator. (all you know is the values for e and pi.)
     
  2. jcsd
  3. Sep 24, 2004 #2

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    well that says that e^pi > e^(e ln(pi)), so since e^x is increasing you just have to show that pi > e ln(pi). so we just need to show that pi/ln(pi) > e.

    but x/ln(x) is increasing for x >=e, and e/ln(e) = e, and pi > e, so pi/ln(pi) > e/ln(e) = e. qed.

    thats cute, i'm gonna try that on my calculus class.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Prove that: e^pi > pi^e, without using a calculator
  1. E, pi, phi (Replies: 65)

  2. E to the pi i (Replies: 5)

  3. Relating pi to e (Replies: 29)

  4. E to i(pi) = -1 (Replies: 11)

Loading...