Re: Problem solving equation
- To: mathgroup at smc.vnet.net
- Subject: [mg40745] Re: Problem solving equation
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Wed, 16 Apr 2003 01:34:47 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <b7gfe0$eba$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi, since when is Log[a+b] == Log[a]+Log[b] ? The correct form of > Log[1.046*Exp[.0151*t]] + Log[1.284*Exp[.0087*t]] == Log[6.3] Log[1.046*Exp[.0151*t] + 1.284*Exp[.0087*t]] == Log[6.3] an that's all. You can factor one exponential term but it still remain that you have to solve a equation like d*t +Log[b+a Exp[q *t]]== c and this can't be done by hand/analytical. Regards Jens Heath wrote: > > Hi, > I'm trying to solve the following equation: > > Solve[1.046*Exp[.0151*t] + 1.284*Exp[.0087*t] == 6.3, t] > > and am getting this error message: > > Solve::"tdep": "The equations appear to involve the variables to be > solved \ > for in an essentially non-algebraic way." > > I cannot solve it with Solve[] or NSolve[]. > I was able to find the solution by using Plot[] to get an idea where > the solution is, followed by FindRoot[]. > > Why doesn't the expression simplify to, as I believe it does on paper, > to: > Log[1.046*Exp[.0151*t]] + Log[1.284*Exp[.0087*t]] == Log[6.3] > Log[1.046]+Log[Exp[.0151*t]]+Log[1.284]+Log[Exp[.0087*t]]==Log[6.3] > Log[1.046*1.284]+.0151*t+.0087*t==Log[6.3] > .0238*t==Log[6.3]-Log[1.046*1.284] > .0238*t==Log[6.3/(1.046*1.284)] > .0238*t==1.545596 > t==64.94 > > This "hand" solution is not the same as the solution I get using > FindRoot[] in Mathematica. Mathematica finds the solution is: > t==82.9182 > > Where am I making an error? Is my hand calculation wrong, or is > Mathematica wrong? Why am I getting an error message using Solve[] or > NSolve[] with Mathematica? > > Thanks, > Heath