Solve for t in terms of a, b, and c: a^t = bc^t

a^t = b(c^t), dividing both sides by c^t, you have now

a^t / c^t = b, using the law of exponents, (x/y)^t = x^t/y^t, then

(a/c)^t = b

take logs of both sides,

log (a/c)^t = log b, [use properties of log]

(t) log (a/c) = log b

(t) (log a - log c) = log b, cross-multiplying, you have

t = (log b)/(log a - log c).

lysserloo, i think this is the answer you are looking for....