Feb 26, 2010 #1 D Delta11 Junior Member level 3 Joined May 14, 2009 Messages 25 Helped 0 Reputation 0 Reaction score 0 Trophy points 1,281 Activity points 1,454 Need help solving a logarithmic equation: (1/x) . exp(-x^2) = 10^-6. Thanks.
Feb 26, 2010 #2 A albbg Advanced Member level 4 Joined Nov 7, 2009 Messages 1,316 Helped 448 Reputation 898 Reaction score 409 Trophy points 1,363 Location Italy Activity points 10,049 If you just need a numerical result, you can use the free math tool Scilab. Code you have to write is: deff('[y]=funct(x)','y=exp(-x^2)/x-1e-6'); [xres]=fsolve(1,funct) from which you will obtain x=3.5426862
If you just need a numerical result, you can use the free math tool Scilab. Code you have to write is: deff('[y]=funct(x)','y=exp(-x^2)/x-1e-6'); [xres]=fsolve(1,funct) from which you will obtain x=3.5426862
Feb 27, 2010 #3 _Eduardo_ Full Member level 5 Joined Aug 31, 2009 Messages 295 Helped 118 Reputation 238 Reaction score 103 Trophy points 1,323 Location Argentina Activity points 2,909 You may solve it by iteratives methods. (1/x) . exp(-x^2) = 10^-6 --> x_n = SQRT(LN(10^6/x_n_1)) Starting with x = 1 converge in few steps to 3.542686172...
You may solve it by iteratives methods. (1/x) . exp(-x^2) = 10^-6 --> x_n = SQRT(LN(10^6/x_n_1)) Starting with x = 1 converge in few steps to 3.542686172...
Mar 1, 2010 #4 D Delta11 Junior Member level 3 Joined May 14, 2009 Messages 25 Helped 0 Reputation 0 Reaction score 0 Trophy points 1,281 Activity points 1,454 Thanx for the help guys. Is there any other approach to solving this problem other than iterative method? Numerical iteration obviously fits but i am looking for a more conventional solution. It is a second order logarithmic equation after all!!!
Thanx for the help guys. Is there any other approach to solving this problem other than iterative method? Numerical iteration obviously fits but i am looking for a more conventional solution. It is a second order logarithmic equation after all!!!
Mar 1, 2010 #5 _Eduardo_ Full Member level 5 Joined Aug 31, 2009 Messages 295 Helped 118 Reputation 238 Reaction score 103 Trophy points 1,323 Location Argentina Activity points 2,909 It cannot be expressed by elementary functions. You need special functions like the Lambert W-function (see Google). If exp(-x^2)/x = a then x = sqrt( W(2/a^2) / 2 ) with W() the Lambert W-function But... to obtain W() you need numerical methods or need software like Mathematica with the ProductLog[z] function...
It cannot be expressed by elementary functions. You need special functions like the Lambert W-function (see Google). If exp(-x^2)/x = a then x = sqrt( W(2/a^2) / 2 ) with W() the Lambert W-function But... to obtain W() you need numerical methods or need software like Mathematica with the ProductLog[z] function...
Jul 29, 2010 #6 A amriths04 Full Member level 5 Joined Jul 15, 2006 Messages 263 Helped 23 Reputation 46 Reaction score 9 Trophy points 1,298 Activity points 2,819 use first few terms(depending on the accuracy) of the taylor's series of the exponential and divide by x. Now it's just solving a polynomial.
use first few terms(depending on the accuracy) of the taylor's series of the exponential and divide by x. Now it's just solving a polynomial.