# Homework Help: Capacitance equation

1. Apr 26, 2006

### dan greig

how would i rearrange this equation to find the capacitance, c?

V=Vo exp(-t/RC)

2. Apr 26, 2006

### daveb

Do you know what the inverse of the exponential function is?

3. Apr 26, 2006

### dan greig

would it go to,

V = Vo ln + (-t/RC)

then to,

V = ln Vo - t x 1/RC

Last edited: Apr 26, 2006
4. Apr 26, 2006

### daveb

You're right that you use the natural log function, but your form is incorrect. What would happen if you take the natural log of the exponential function, or ln(e^x) = ?

5. Apr 26, 2006

### dan greig

ln(e) + x ?????

not really sure you've lost me a bit sorry

6. Apr 26, 2006

### Staff: Mentor

Let's do it first with the more familiar base 10.

log( 10^2 ) = 2 (right?)

log( 10^x ) = ?

ln( e^x ) is analogous to log( 10^x )...

7. Apr 26, 2006

### dan greig

log(10^x) = x ?

analogous?? The same as??

but log e = 1

does that mean log e^x = 1^x ?

therefore log e^x = x ?

Last edited: Apr 26, 2006
8. Apr 26, 2006

### Staff: Mentor

No, you need to keep your log() and ln() straight. log() is used with base 10 math, and ln() is used with base e math.

log( 10^x ) = x

ln( e^x ) = ?

Try a few numbers on your calculator to help you keep it straight. There's a reason that most calculators overload the log() key with 10^x and overload the ln() key with e^x.....

9. Apr 27, 2006

### Reshma

How come you did not take the natural log on the left hand side? :surprised
If this is your original equation, then:
$$\ln V = \ln V_0 - {t\over RC}$$

Furthur evaluation is simple.