I have the following function : $be^{-at} -ae^{-bt} =0.5(b-a)$ where b and a is know and I want to solve for t. I tried several ways to simplify it but still cannot find a way to get $t$. Any suggestion will be helpful. Thanks.
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Let $x=e^{-t}$ and you will get a polynomial of generic degree. Such polynomials usually cannot be solved in general. However, the result here looks oddly symmetric, so there may be a possibility... – Simply Beautiful Art Aug 04 '17 at 16:44
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@SimplyBeautifulArt: what if $a$ or $b$ is not an integer or natural number? – Robert Lewis Aug 04 '17 at 16:55
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1@RobertLewis Then that's even worse to solve :-) – Simply Beautiful Art Aug 04 '17 at 17:13
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@SimplyBeautifulArt: true enough! – Robert Lewis Aug 04 '17 at 17:14
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hint
divide by $ab $ to get
$$\frac {e^{-at}-0.5}{a}=\frac {e^{-bt}-0.5}{b} $$
hamam_Abdallah
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