Re: Exponential Equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg29808] Re: Exponential Equations*From*: Erich Mueller <emuelle1 at uiuc.edu>*Date*: Wed, 11 Jul 2001 01:26:57 -0400 (EDT)*Organization*: University of Illinois at Urbana-Champaign*References*: <9hetrp$6ku$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

The exponential function is periodic in the complex plane. The equation that you give has an infinite number of solutions, x=-1+(n/7) Pi I, for integer n, so you should not be surprised to find multiple solutions. Mathematica's equation solving algorithm is made for solving algebraic equations, so it solves your problem by factoring a seventh order polynomial in Exp[x] -- hence the seven solutions. only finds 7 of the solutions. On Thu, 28 Jun 2001, Shippee, Steve wrote: > If this is too basic of a question for the "LIST", please respond to me > directly via email at shippee at jcs.mil and thanks in advance for any > assistance provided. I'd be happy to provide you a "notebook", too, if that > would help. > > With the equation e^5x = 1/e^2x + 7 [e is the mathematical e = 2.718] > > If I use Solve[e^5x == 1/e^2x + 7] I do not get an appropriately traditional > answer. The RHS of the equation is the mathematical "e" to the power of 2x > + 7. > > Using the equation e^5x = 1/e^2x + 7 It appears to me Mathematica is > skipping the step > > e^5x = e^-(2x + 7 ) > > which would result in > > 5x = -(2x + 7) > 5x = -2x - 7 > 7x = -7 > x = -1 > > Because with Mathematica I kept getting the answer: > > Out[1]= \!\({{x \[Rule] Log[Root[\(-1\) + 7\ #1\^5 + #1\^7 &, 1]]}, {x > \[Rule] Log[Root[\(-1\) + 7\ #1\^5 + #1\^7 &, 2]]}, {x \[Rule] > Log[Root[\(-1\) + 7\ #1\^5 + #1\^7 &, 3]]}, {x \[Rule] Log[Root[\(-1\) + 7\ > #1\^5 + #1\^7 &, 4]]}, {x \[Rule] Log[Root[\(-1\) + 7\ #1\^5 + #1\^7 &, > 5]]}, {x \[Rule] Log[Root[\(-1\) + 7\ #1\^5 + #1\^7 &, 6]]}, {x \[Rule] > Log[Root[\(-1\) + 7\ #1\^5 + #1\^7 &, 7]]}}\) > > Before trying all of the above, I loaded: > << Graphics`Graphics` > << Algebra`AlgebraicInequalities` > << Algebra`InequalitySolve` > << Algebra`RootIsolation` > >

**Follow-Ups**:**Re: Re: Exponential Equations***From:*"J Rockmann" <mtheory@msn.com>