a = (1-e^(bt))/(1-e^(ct))

Isolate t (a, b, c are all known).

Anyone? :)

If you are curious as to why I need to solve this - I am trying to determine the parameters of an exponential decay given 3 points.

V = Vf - (Vf - Vi)e^(-t/r)

where r is the time constant.

(this is the transient response of a battery after a charging current or a load has been removed)

After solving the system (3 V's and 3 t's), I got an equation in the form above, and couldn't solve it.