I have tried solving by using Taylor's series expansion for $e^x$ and approximating till the third term of the expansion (i.e. term with power 2). This gave me a quadratic equation which was easy to solve. But I am using the solution of this equation as part of a bigger numerical simulation using Finite Difference method. And the small error due to approximation in the expansion for $e^x$ accumulated over many iterations and gave erroneous results in the end.

So, I need some other way of solving this equation that does not involve approximation.

  • $\begingroup$ you will Need a nmerical method, some sprecial cases can you solve symbolically $\endgroup$ – Dr. Sonnhard Graubner May 21 '17 at 7:18
  • $\begingroup$ Dr. Sonnhard Graubner, could you elaborate on this ? I am using the Block Newton method. $\endgroup$ – P. Biswas May 21 '17 at 7:41
  • $\begingroup$ Also, someone told me that the solution for this equation can be given Lambert function. Is this possible ? $\endgroup$ – P. Biswas May 21 '17 at 7:42
  • $\begingroup$ no solution is found in Lamberd function here, try Wolfram alpha $\endgroup$ – Dr. Sonnhard Graubner May 21 '17 at 7:43
  • $\begingroup$ see here for the Newton method keisan.casio.com/exec/system/1244946907 $\endgroup$ – Dr. Sonnhard Graubner May 21 '17 at 7:44

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