Can someone help me solve this one? All I need to do is to isolate x in the following equation:

$\ e^{-x/t}+e^{-x/z}=1-\frac{2}{e}$

t and z are real numbers, yet unknown.


  • $\begingroup$ Mathematica returns nothing. I'm fairly convinced there is no simple solution. $\endgroup$ – Brevan Ellefsen May 27 '17 at 15:59

This is of the form $a^x+b^x = c$ which can only be solved numerically in general.

Answer to original question:

Since $2/e < 1$ and $e^z > 0$ for all real $z$, the left side is always positive and the right side is negative so there are no solutions.

  • $\begingroup$ Sorry Marty that was a typo. I have corrected it now. Was supposed to be the other way around $\endgroup$ – HJRO May 27 '17 at 16:04
  • $\begingroup$ Good point though! $\endgroup$ – HJRO May 27 '17 at 16:05
  • $\begingroup$ Would you happen to have a source on that? $\endgroup$ – HJRO Jul 21 '17 at 6:58

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