HP 50G "Bad Argument Value"

[root07]

SOLVE(X^40=13^X,X) -> SOLVE Error: Bad Argument Value.
How to solve the equation?

[Joe Horn]

I'd suggest using the numeric solver (ROOT) instead of SOLVE or SOLVEVX because those use CAS logic to look for a symbolic result. ROOT uses numeric methods to find one root at a time near a given initial guess.

In RPN mode:
'X^40=13^X'
'X'
1 (or whatever guess you want to start at)
ROOT --> 1.07109628939

With an initial guess of -1 you get another root, -0.941418703497

Also try an initial guess of 65. Finding ALL the roots is left as an exercise for the student. ;-)

[BartDB]

You can also use the interactive numerical solver:

Red Shift NUM.SLV, then select 1. Solve equation
(Initial guesses can be entered for X before selecting F6:SOLVE)

This is useful if you want to quickly try just a few guesses.

However, the ROOT command can be used in a program (for example if you wish to create a program that tries a several guesses (for instance it has an input for both the equation and a list of guesses)).