November 8th, 2012, 11:19 AM  #1 
Joined: Nov 2012 Posts: 4 Thanks: 0  e^x3x=0
What type of solution does e^x3x=0 have? a finite number, a surd, a fraction, a combination of constants? 
November 8th, 2012, 11:31 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 13,911 Thanks: 389 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic  Re: e^x3x=0
I believe you need Lambert's W function for this problem, so I would call it a transcendental solution. There should be two realvalued solutions (and infinitely many complex solutions).

November 8th, 2012, 11:41 AM  #3 
Joined: Nov 2012 Posts: 4 Thanks: 0  Re: e^x3x=0
and can it be written down accurately? for example pi is transcendental, but we can write be instead of 3.14159.... Does the same happen with the solution of x?

November 8th, 2012, 12:15 PM  #4  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,866 Thanks: 81 Math Focus: Number Theory  Re: e^x3x=0 Quote:
 
November 8th, 2012, 12:17 PM  #5 
Global Moderator Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 11,746 Thanks: 204 Math Focus: The calculus  Re: e^x3x=0
You can find as many digits as you wish by using a root finding technique such as Newton's method.

November 8th, 2012, 02:32 PM  #6  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 13,911 Thanks: 389 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic  Re: e^x3x=0 Quote:
 
November 11th, 2012, 08:41 AM  #7 
Joined: Oct 2012 Posts: 22 Thanks: 0  Re: e^x3x=0
e^x3x=0 e^x=3x e^x=(1/3x) powering both sides to (1/3x) e^(x * (1/3x))=(1/3x)^(1/3x) e^(1/3)=(1/3x)^(1/3x) then 1/3x = ssrt(e^(1/3)) , ssrt is super sequare root used in tetration. ssrt (z) = 1/(z^^n) when n goes to infinity then x = 1/(3*(ssrt(e^(1/3)))) 
November 11th, 2012, 08:44 AM  #8 
Joined: Oct 2012 Posts: 22 Thanks: 0  Re: e^x3x=0
correction ssrt (z) = 1/((1/z)^^n) when n goes to infinity 
November 11th, 2012, 10:33 AM  #9  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 13,911 Thanks: 389 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic  Re: e^x3x=0 Quote:
 
November 11th, 2012, 02:24 PM  #10  
Joined: Oct 2012 Posts: 22 Thanks: 0  Re: e^x3x=0 Quote:
but ssrt(x) is elementry tool because looks like srt(x). that is why I prefer ssrt(x) than W(x).  

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