Other Equations

In addition to being able to solve purely algebraic equations, Mathematica can also solve some equations involving other functions. Solve can be used in solving radical equations, equations involving trigonometric or hyperbolic functions and their inverses, as well as equations involving exponentials and logarithms. As a reminder, its syntax is NSolve[eqns, vars], where eqns is your equation or set of equations and vars is the variable(s) in the equation(s).

Algebraic Solutions

Radical Equations

Note that in radical equations, Solve discards parasite solutions. To see all candidate solutions, including parasites, set VerifySolutions to False.


Equations Involving Trigonometric or Hyperbolic Functions and Their Inverses

Equations Involving Exponentials and Logarithms

More information on Solve is available.

Numeric Solutions

If your equations involve only linear functions or polynomials, then you can use NSolve to get numerical approximations to all the solutions. However, when your equations involve more complicated functions, there is, in general, no systematic procedure for finding all solutions, even numerically. In such cases, you can use FindRoot to search for solutions. The basic syntax for FindRoot is FindRoot[eqn, {x, [Graphics:../Images/index_gr_33.gif]}] where eqn is the equation you are solving and [Graphics:../Images/index_gr_34.gif] is the value around which FindRoot starts its search.

 FindRoot[3Cos[x] == Log[x], {x, 1}]

More information on FindRoot is available.