Re: How to solve this equation?
- To: mathgroup at smc.vnet.net
- Subject: [mg103533] Re: [mg103518] How to solve this equation?
- From: danl at wolfram.com
- Date: Sun, 27 Sep 2009 07:30:46 -0400 (EDT)
- References: <200909261013.GAA23377@smc.vnet.net>
> Hi, > > Can anyone tell me how to solve a^{-x}+b^{-x}+c^{-x}==0 for x, where a and > b and c are some constants. > > Yours, > > Jamil. For given numeric constants, could use FindRoot to get one solution. In[123]:= FindRoot[Pi^(-x) + E^(-x) + Catalan^(-x) == 0, {x, .1 + I}] Out[123]= {x -> 0.581515 + 2.71516 I} Or could use reduce, to get all roots in some region. In[12]:= Reduce[Pi^(-x) + E^(-x) + Catalan^(-x) == 0 && Abs[x] < 5, x] Out[12]= x == Root[{1 + E^(-(1 - Log[\[Pi]]) #1) + E^(-(Log[Catalan] - Log[\[Pi]]) #1) &, 0.581514699561345300020023543344396616265085370855763 - 2.715155022486549482573351321493738583224908371244565 I}] || x == Root[{1 + E^(-(1 - Log[\[Pi]]) #1) + E^(-(Log[Catalan] - Log[\[Pi]]) #1) &, 0.581514699561345300020023543344397 + 2.715155022486549482573351321493739 I}] This result can be viewed as local root-finding plus validation, meaning it gives all roots in the specified region. A caveat is the region must only contain finitely many roots. Daniel Lichtblau Wolfram Research
- References:
- How to solve this equation?
- From: Jamil Ariai <j_ariai@hotmail.com>
- How to solve this equation?