Re: Solving equations involving Ln function
- To: mathgroup at smc.vnet.net
- Subject: [mg19907] Re: Solving equations involving Ln function
- From: adam.smith at hillsdale.edu
- Date: Tue, 21 Sep 1999 02:22:44 -0400
- References: <7s1pb3$9n9@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
You want to use PowerExpand[]. I have included the code below. It is worth noting that Simplify[] does not automatically use PowerExpand and that is why the form Simplify[PowerExpand[g]] is used. There can be other times when it is necessary to perform something similar to PowerExpand[] before simplifying. Adam Smith In[1]:= g = Log[x]+delta*v == Log[(1-delta)*x/(1-delta^2)]+delta*Log[(1-delta) *delta*x/(1-delta^2)]+delta^2*v Out[1]= 2 (1 - delta) x delta v + Log[x] == delta v + Log[-------------] + 2 1 - delta (1 - delta) delta x delta Log[-------------------] 2 1 - delta In[2]:= PowerExpand[g] Out[2]= 2 delta v + Log[x] == delta v + Log[1 - delta] - 2 Log[1 - delta ] + Log[x] + 2 delta (Log[1 - delta] + Log[delta] - Log[1 - delta ] + Log[x]) In[3]:= newg = Simplify[PowerExpand[g]] Out[3]= 2 delta v - delta v - (1 + delta) Log[1 - delta] - 2 delta Log[delta] + Log[1 - delta ] + 2 delta Log[1 - delta ] - delta Log[x] == 0 In[4]:= Solve[newg,x] Out[4]= 2 {{x -> Power[E, (delta v - delta v - Log[1 - delta] - delta Log[1 - delta] - delta Log[delta] + 2 2 Log[1 - delta ] + delta Log[1 - delta ])/delta]}} In[5]:= Simplify[%] Out[5]= 2 1/delta v - delta v (1 + delta) (1 - delta ) E {{x -> --------------------------------------------}} 1/delta (1 - delta) delta In article <7s1pb3$9n9 at smc.vnet.net>, Satyajit Bose <sgb2 at columbia.edu> wrote: > Hello, > > I am trying to solve some equations involving the natural log function. > Mathematica 3.0 will not let me solve them since the relations are > non-algebraic. Is there any way to restrict the domain to positive reals > or get Mathematica to use the exponential as an inverse, so that I can > get a solution. I know that this can be done in another system, presumably > because it is less careful about atypical domain restrictions. Here is > my input line and results in the kernel: > > In[1]:= > Solve[Log[x]+delta*v==Log[(1-delta)*x/(1-delta^2)]+delta*Log[(1-delta) *d > > elta*x/(1-delta^2)]+delta^2*v,x] > > Solve::tdep: The equations appear to involve transcendental functions of > the > variables in an essentially non-algebraic way. > > Out[1]= Solve[delta v + Log[x] == > > 2 (1 - delta) x (1 - delta) delta x > > delta v + Log[-------------] + delta Log[-------------------], x] > > 2 2 > 1 - delta 1 - delta > > I am hoping to get a solution that looks like this: > > x -> exp[v*(1-delta)]*(1+delta)^(1+1/delta)/delta) > > Thank you for all your help. > > Sayajit Bose > -- > Satyajit Bose > Department of Economics New York, NY 10027 > Columbia University (212) 665-8208 > http://www.columbia.edu/~sgb2 sgb2 at columbia.edu > > Sent via Deja.com http://www.deja.com/ Share what you know. Learn what you don't.