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I'm trying to find a root of the following equation $$\theta^\frac{t}{s}-\theta-\sqrt{1-p},$$ where $0<t\leq1\leq s$ and $0<p<1$. I've tried FindRoot and Reduce, but somehow they don't process the output.

Using reduce function, what I tried is

Reduce[theta^(t/s) - theta - Sqrt[1 - p] == 0 && theta > 0 && theta < 1 &&0 < t<=  1<=s && 0 < p < 1, theta]

Any suggestions on how to solve for a symbolic function?

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    $\begingroup$ Related: mathematica.stackexchange.com/questions/139881/… $\endgroup$ – Michael E2 Dec 9 '18 at 17:52
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    $\begingroup$ @MichaelE2 has given you the answer. Probably the best you can do is solve explicitly for the exponent: $\frac{r}{s}\to \frac{\log \left(\theta +\sqrt{1-p}\right)}{\log (\theta )}$. $\endgroup$ – JimB Dec 9 '18 at 18:58
  • $\begingroup$ What is the unknown? $\endgroup$ – Αλέξανδρος Ζεγγ Dec 10 '18 at 3:18
  • $\begingroup$ $\theta$ is the unknown and I want to find roots (probably there will be two of them) of the above equation. All the rest is just parameters. I've tried by simplifuying the equation into $\theta^a-\theta-b$, where $a=\frac{t}{s}$ and $b=\sqrt{1-p}$, but still just don't know how to solve for roots... $\endgroup$ – Greenteamaniac Dec 10 '18 at 5:08
  • $\begingroup$ This is not the type of equations for which I would expect symbolic solutions.Try numerics. $\endgroup$ – Mariusz Iwaniuk Dec 10 '18 at 7:30

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