Register to reply

Natural logarithm and pi... help?

by Guero
Tags: logarithm, natural
Share this thread:
Guero
#1
Apr10-05, 09:49 AM
P: 15
I haven't been able to prove:

ln(e)/e > ln(pi)/pi

without calculating any of the values. Help would be much appreciated.
Phys.Org News Partner Science news on Phys.org
'Smart material' chin strap harvests energy from chewing
King Richard III died painfully on battlefield
Capturing ancient Maya sites from both a rat's and a 'bat's eye view'
arildno
#2
Apr10-05, 09:52 AM
Sci Advisor
HW Helper
PF Gold
P: 12,016
Hint:
Consider the function
[tex]f(x)=\frac{ln(x)}{x}}[/tex],
with domain the positive real half-axis.

Determine the function's maximum value.
Guero
#3
Apr10-05, 09:58 AM
P: 15
mm, I can see that, but I was looking for a proof that shows that e^pi > pi^e

arildno
#4
Apr10-05, 10:09 AM
Sci Advisor
HW Helper
PF Gold
P: 12,016
Natural logarithm and pi... help?

Well, since you can prove that ln(e)/e is the maximum value for f, we also have:
[tex]\pi(ln(e))>eln(\pi)\to{ln}(e^{\pi})>ln(\pi^{e})[/tex]
wherefrom your inequality follows.
Guero
#5
Apr10-05, 10:13 AM
P: 15
Argh! I get it, Thanks!

I feel pretty stupid now.


Register to reply

Related Discussions
Natural Logarithm of Negative Numbers General Math 5
Intermediate algebra , Natural logarithm question General Math 11
Natural Logarithm Manupulations Precalculus Mathematics Homework 2
Natural Logarithm Derivative question Calculus & Beyond Homework 1
Natural logarithm of negative numbers Introductory Physics Homework 8