Need help solving for a variable in exponent

[johnczerwinski]

I'm stuck in solving for "t" in the following equation. Any help and pointing me to some refresher resources on solving these types of problems would be greatly appreciated!

Vc = Vs(1-e^(-t/rc))

Here's what I've done so far
Vc = 1.27
Vs = 8.35
r = 10,000
c = .001

(1). Vc = Vs(1-e^(-t/rc))
(2). 1.27 = 8.35(1-e^(-t/(10,000 x .001)))
(3). 1.27/8.35 = 1 - e^(-t/10)
(4). 1 - .152 = -e^(-t/10)
(5). .848 = -e^(-t/10) <-- I'm stuck here...

 

[lev888]

I'm stuck in solving for "t" in the following equation. Any help and pointing me to some refresher resources on solving these types of problems would be greatly appreciated!

Vc = Vs(1-e^(-t/rc))

Here's what I've done so far
Vc = 1.27
Vs = 8.35
r = 10,000
c = .001

(1). Vc = Vs(1-e^(-t/rc))
(2). 1.27 = 8.35(1-e^(-t/(10,000 x .001)))
(3). 1.27/8.35 = 1 - e^(-t/10)
(4). 1 - .152 = -e^(-t/10)
(5). .848 = -e^(-t/10) <-- I'm stuck here...

Enter "solving for a variable in exponent" in google search.

I understand if you are stuck on a particular problem, but not making even a slight effort to find how to solve a whole category of problems...

 

[Deleted member 4993]

I'm stuck in solving for "t" in the following equation. Any help and pointing me to some refresher resources on solving these types of problems would be greatly appreciated!

Vc = Vs(1-e^(-t/rc))

Here's what I've done so far
Vc = 1.27
Vs = 8.35
r = 10,000
c = .001

(1). Vc = Vs(1-e^(-t/rc))
(2). 1.27 = 8.35(1-e^(-t/(10,000 x .001)))
(3). 1.27/8.35 = 1 - e^(-t/10)
(4). 1 - .152 = -e^(-t/10)
(5). .848 = -e^(-t/10) <-- I'm stuck here...

(1). Vc = Vs(1-e^(-t/rc))
(2). 1.27 = 8.35(1-e^(-t/(10,000 x .001)))
(3). 1.27/8.35 = 1 - e^(-t/10)
(4). 1 - .152 = -e^(-t/10) ......................................check this step for sign mistake (or accuracy)

 

[johnczerwinski]

Enter "solving for a variable in exponent" in google search.

I understand if you are stuck on a particular problem, but not making even a slight effort to find how to solve a whole category of problems...

Actually, I did make an effort. Just needed help on the exponent part.

So to expand on your comment...without Googling, which I do know how to do but maybe didn't know the right search phrase, was to raise both sides of the equation by 10, then take the natural log of -e^(-t). I believe I have the right answer as I've checked other sources.

Thanks anyway.

 

[HallsofIvy]

I'm stuck in solving for "t" in the following equation. Any help and pointing me to some refresher resources on solving these types of problems would be greatly appreciated!

Vc = Vs(1-e^(-t/rc))

Here's what I've done so far
Vc = 1.27
Vs = 8.35
r = 10,000
c = .001

(1). Vc = Vs(1-e^(-t/rc))
(2). 1.27 = 8.35(1-e^(-t/(10,000 x .001)))
(3). 1.27/8.35 = 1 - e^(-t/10)
(4). 1 - .152 = -e^(-t/10)

This is where your mistake is. To get rid of the "1" on the right in "1- e^{-t/10)" you need to subtract 1 from each side. You should have
.152- 1= -e^(-t/10) so that -.848= -e^{-t/10}
Then multiply both sides by -1 to get
.848= e^{-t/10}.

Of course now you take the logarithm of both sides.

(5). .848 = -e^(-t/10) <-- I'm stuck here...