Can I analytically solve a logarithmic equation using the symbolic toolbox?
6 vues (au cours des 30 derniers jours)
Afficher commentaires plus anciens
Anik Faisal
le 19 Mar 2019
Réponse apportée : John D'Errico
le 20 Mar 2019
I have an equation : where A is a constant. I have tried to solve this equation for 'u' with the symbolic toolbox. I am getting the following error:
Warning: Unable to find explicit solution. For options, see help.
In solve (line 317) . Any suggestions how the equation can be solved?
syms u A
eqn=u/(log(u)+1)-A==0;
solve(eqn,u)
0 commentaires
Réponse acceptée
John D'Errico
le 20 Mar 2019
Sigh. Sorry. I typed too fast there, and I answered incorrectly. Not sure why solve does not get this.
Multiply by log(u) + 1. Valid as long as u is not 1/e.
u = A*(log(u) + 1)
Transform this using x = log(u) + 1. Then u = exp(x - 1) = exp(x)/exp(1). Our problem is now:
exp(x)/exp(1) = A*x
or
exp(x) = exp(1)*A*x
Solve seems to see how to do that.
syms x A
xsol = solve(exp(x) == exp(1)*A*x,x)
xsol =
-lambertw(0, -1125899906842624/(3060513257434037*A))
usol = exp(xsol - 1)
usol =
exp(- lambertw(0, -1125899906842624/(3060513257434037*A)) - 1)
Verify this satisfies the original problem.
vpa(simplify(subs(u/(log(u)+1)-A,u,usol)))
ans =
0.00000000000000011018891328384950189261640307115*A
It looks like solve used a floating point approximation for exp(1) in there, so we still got zero, plus some floating point trash.
0 commentaires
Plus de réponses (0)
Voir également
Catégories
En savoir plus sur Assumptions dans Help Center et File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!