I would like to solve the equation:

A Exp[m t + s Sqrt[t] x - 1/2 s^2 t] >= K

with respect to x (which is in the exponent) using Mathematica. All parameters are positive. Of course, the answer is easy to get by hand. However, for some reason I could not figure out how to do it with Mathematica. What I tried gave me some error messages.

Also, I would like the solution to be expressed without all those conditionals. That is, I want the answer in which all the parameters satisfy whatever they need to satisfy so that the generic solution holds,

I would greatly appreciate help in figuring out how to do this.

  • 2
    $\begingroup$ "gave me some error messages when I tried" — Please show us what you've tried. $\endgroup$
    – rm -rf
    Jan 18, 2013 at 23:45
  • $\begingroup$ A kickstart Reduce[a Exp[m t + s Sqrt[t] x - 1/2 s^2 t] >= k, x, Reals] $\endgroup$ Jan 18, 2013 at 23:49
  • $\begingroup$ Note how @belisarius replaced K A with k a, this is because things starting with an upper-case letter are reserved for built-in functionality and it's good practice to avoid that or it will bite you in the ass $\endgroup$
    – ssch
    Jan 18, 2013 at 23:57
  • $\begingroup$ Tried it before, but get totally wrong solution. Have you tried it? Works OK if I replace Sqrt[t] with some variable say p, but still get huge mess of an expression (lots of extra conditions. $\endgroup$
    – Branko
    Jan 18, 2013 at 23:58
  • 1
    $\begingroup$ @ssch Not precisely true. Capital letters are used by a lot of third party packages, also, and there is nothing in the language that prevents this. It is a good recommendation, though, and if you decide not to follow it, you need to be careful. For the most part, I choose to ignore it, and capitalize my function names and lower case is used for my variable names. $\endgroup$
    – rcollyer
    Jan 19, 2013 at 3:02

1 Answer 1


If you replace k-> koa, a->1, Sqrt[t]->tt (since they're all positive parameters) then

Reduce[{ Exp[m tt^2 + s tt x - 1/2 s^2 tt^2] >= koa, m > 0, tt > 0, s > 0, koa > 0}, x, Reals]

(* koa > 0 && m > 0 && s > 0 && tt > 0 && 
   x >= (-2 m tt^2 + s^2 tt^2 + 2 Log[koa])/(2 s tt) *)

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.