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My problem is this:
Solve for t in terms of a, b, and c: a^t = bc^t
So far I've gotten this:
t loga = t logbc
t loga = t(logb + logc)
I don't know if that's right, and if that is right, where to go from there. I'm also not even sure what the problem is asking me to do! Do I need three solutions?
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....
AH! I never considered sectioning off c^t from b! I was treating it as (bc)^t, which it's not.
Thank you SO much! I completely understand this now. (Clapping)
Yes, bc^t = b(c^t) not bc^t = (bc)^t.