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## Which of the quantities is greater, e^&#960; or &#960;^e?

e^&#960; 25 62.5%
&#960;^e 11 27.5%
They are equal 4 10%
Voters 40 .

### For you Math Folks: WITHOUT A CALCULATOR, Which is Greater: e^π or π^e ?

X5TeRraN

Member

YOU CANNOT USE A CALCULATOR OR ANY KIND OF MECHANICAL DEVICE TO SOLVE THIS PROBLEM. Only pencil, paper and your brain.

You're welcome to leave your thoughts in the posts below if you so feel like it. Good luck!

Jamaree

Senior Member

Screw you, I'm a cheater.

e^pi is greater.

SPIKE SPlEGEL

Senior Member

π^e

work? just like all my other math tests

I ****ING GUESSED

Bakabridget

Senior Member

What is e?

X5TeRraN

Member

Quote:
Jamaree:
Screw you, I'm a cheater.

Aw come on it's a fun little math exercise! It will make you smarter!

Jamaree

Senior Member

Quote:
X5TeRraN:
Aw come on it's a fun little math exercise! It will make you smarter!

Screw smarts, I have been studying the last five hours, about to go to work for three, my brain needs to be turned off.

Umbasa

Senior Member

e is like 2.2 or something, im guessing e^pie

Darkvolcan

Senior Member

Doing it from my head and rounding off and stuff, I figured e^pi.

I forgot what I did exactly, but I checked google and it said I was right, so yeah.

Navvan

Senior Member

lπ(ln(e^&#960) =lπ(π*ln(e))= lπ(&#960=1
lπ(ln(π^e)) = lπ(e*ln(&#960)=lπ(e)+lπ(lπ(&#960)=lπ(e)
e<π implies lπ(e)<lπ(&#960=1 thus e^π>π^e

Think that is sound

lπ is a logarithm with a base of π if it wasn't clear