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....