Solving an RC Circuit: Find Time to Reach 65% of Max Value

[Parad0x88]

Homework Statement

An RC circuit has EMF=12.0V, R=15 kΩ and C=3.8 μF. How long does it take for energy stored in the capacitor to reach 65% of its maximal value?

Homework Equations

1) Q = Cε
2) Q X .65 = desired charge
3) q(t) = Q(1 - e^-t/RC)

The Attempt at a Solution

This is fairly straightforward to be honest, but I just don't know how to isolate for t in formula 3.

1) Q = 12v X 3.8μf = 4.56 X 10^-5 C
2) Q X .65 = 4.56 X 10^-5 C X .65 = 2.964 X 10^-5
3) q(t) = 2.964 X 10^-5(1 - e^-t/0.057)

First question: Is that how I have to write down the formula with the known values?
Second question: How do I isolate for t?


Thank you!

Edit: Here is what I found by browsing on the Internet:

0.65Q = Q(1 - e^-t/RC, or 0.65 = 1 - e^-t/RC
-.35 = -e^-t/RC
.35 = e^-t/RC
ln .35 = -t/RC
t = -ln(.35) * RC
t = 1.0498 * 0.057
t = 0.0598 seconds

 

[CWatters]

Deleted as you found the answer.