Re: Problem solving equation
- To: mathgroup at smc.vnet.net
- Subject: [mg40757] Re: Problem solving equation
- From: wself at msubillings.edu (Will Self)
- Date: Wed, 16 Apr 2003 01:37:09 -0400 (EDT)
- References: <b7gfe0$eba$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
heathdwatts at hotmail.com (Heath) wrote in message news:<b7gfe0$eba$1 at smc.vnet.net>... > 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 Your hand calculation is wrong. You are using the rule Log[a+b]->Log[a]+Log[b], which is wrong. When Solve or NSolve doesn't work, your method of graphing and then using FindRoot is an excellent approach. Will