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Error solving an equation: no methods available

Posted 3 months ago
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Hi all, I hope you all are fine and safe Can anyone help me to solve this equation?

Reduce[{E^(-a x - b x^\[Gamma]) - c == 0, a > 0, b > 0, \[Gamma] > 0, 
c > 0}, x]

Thanks in advance

It is a trascendental equation with parameters. The main problem is the symbolic exponent \[Gamma]. We don't get a symbolic solution for this either:

Solve[ x + x^\[Gamma] == 1 && \[Gamma] > 0, x]
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