Analytic solution to a*t^x + b*t^y + c*t^z + d = 0 for t?

Or, is this known to be possible, impossible or unkown? Another form is a*x^t + b*y^t + c*z^t + d = 0, of course for different constants a, b, c, d, x, y, and z. Ultimatelly i'm looking for the solution of a*exp(-t*x) + b*exp(-t*y) + c*exp(-t*z) + d = 0 for t %26gt;= 0, also where a, b.. etc are different constants to the previous formulas, and x, y, z %26gt; 0.

Analytic solution to a*t^x + b*t^y + c*t^z + d = 0 for t?
Note that if x = 5 and y and z are integers between 1 and 4, then if there were a closed form solution for the t^x case, you'd have a closed form solution for many quintic equations, and no such form is known.





So no guarantees, but I would guess impossible.

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