# Exponent Problem

• Sep 2nd 2009, 10:37 PM
lysserloo
Exponent Problem
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?
• Sep 2nd 2009, 11:23 PM
pacman
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....
• Sep 3rd 2009, 12:08 AM
lysserloo
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)
• Sep 3rd 2009, 06:31 AM
pacman
Yes, bc^t = b(c^t) not bc^t = (bc)^t.