How to solve for t in exponential function

Question

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.

Answer 1

hint

divide by $ab $ to get

$$\frac {e^{-at}-0.5}{a}=\frac {e^{-bt}-0.5}{b} $$