Any appreciated...

[Laikule]

I'm stuck on the attached question.

I know I have to isolate C on one side using logs as inverse of the exponential e, but not sure how to.

Any help is appreciated!

 

[MarkFL]

Hello, and welcome to FMH!

The first thing I would do is divide through by \(V_S\) to obtain:

[MATH]\frac{V_C}{V_S}=1-e^{-\frac{t}{RC}}[/MATH]
And then arrange this as:

[MATH]e^{-\frac{t}{RC}}=1-\frac{V_C}{V_S}[/MATH]
Or:

[MATH]e^{-\frac{t}{RC}}=\frac{V_S-V_C}{V_S}[/MATH]
Invert both sides:

[MATH]e^{\frac{t}{RC}}=\frac{V_S}{V_S-V_C}[/MATH]
Next, convert from exponential to logarithmic form...can you proceed?

 

[Laikule]

Hi, thank you!

And thank you very much for your help!

I'm still a little stuck, sorry.

How would I isolate the C from T/RC after taking the log of both sides?
Do I multiply by R?

This is where I'm at...

 

[MarkFL]

I would multiply both sides by:

[MATH]\frac{C}{\log_e\left(\frac{V_S}{V_S-V_C}\right)}[/MATH]...