Calculus Calculus Math Forum

 December 14th, 2016, 07:37 AM #1 Newbie   Joined: Dec 2016 From: Germany, Magdeburg Posts: 3 Thanks: 0 Solving e^x - x = a What's the mechanism for solving an equation of this kind? Last edited by skipjack; December 17th, 2016 at 04:37 AM. December 14th, 2016, 08:00 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,632 Thanks: 1472 You're going to have to solve this numerically. There is a closed form solution $x = -W\left(-e^{-a}\right)-a$ where $W(x)$ is the Lambert W function but $W(x)$ doesn't generally show up on your calculator. There are no lack of numerical algorithms to solve equations like this. Newton's method is a good place to start. Thanks from topsquark and knownothing1994 December 14th, 2016, 08:13 AM #3 Newbie   Joined: Dec 2016 From: Germany, Magdeburg Posts: 3 Thanks: 0 Thanks a lot! I'll start with learning about the Lambert function and the Newton method. Last edited by skipjack; December 14th, 2016 at 11:35 AM. December 16th, 2016, 05:59 PM #4 Member   Joined: Dec 2016 From: - Posts: 62 Thanks: 10 This is a trascendental equation, where the function on the left equals the function on the right: \begin{eqnarray} e^{x}=x+a \end{eqnarray} The solution is calculated graphically, by plotting both functions as a function of $x$. All possible solutions to the equation are then those values of $x$ where both graphs cross. December 17th, 2016, 04:48 AM #5 Global Moderator   Joined: Dec 2006 Posts: 21,105 Thanks: 2324 If $a$ < 1, there is no real solution. If $a$ = 1, $x$ = 0 is the only real solution. If $a$ > 1, there are two real solutions. Tags equation, euler, solving Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post yogazen2013 Algebra 6 October 5th, 2013 05:02 AM aaron-math Algebra 1 September 13th, 2012 11:56 PM missingblood Algebra 1 January 20th, 2012 09:32 PM mroberso13 Calculus 8 December 31st, 1969 04:00 PM missingblood Calculus 1 December 31st, 1969 04:00 PM

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