Question

Quick algebra question.

Answer 1

I need to rearrange this equation in terms of Vw.

Answer 2

I am supposed to get this equation from doing so.

Answer 3

However, we doing this myself. I get the following. Vw=-V0ln(cf/c0)

Answer 4

^
That is the answer I get as well.

Answer 5

Hmm..There must be an issue with my notes..It might be a completely different equation..

Answer 6

\[C_f= C_0e^{-\dfrac{V_w}{V_0}}\]
ln both sides:
\[ln C_f= ln (C_0e^{-\dfrac{V_w}{V_0}})= ln C_0 + ln e^{-\dfrac{V_w}{V_0}} = ln C_0 - {\dfrac{V_w}{V_0}}\]
therefore, \[\dfrac{V_w}{V_0}= ln C_0-ln C_f= ln \dfrac{C_0}{C_f} \]
\[V_w = V_0ln \dfrac{C_0}{C_f} \]
why do you guys get -?

Answer 7

Thank you @Loser66. I'm a bit rusty at this!