# Help With Transpositon Involving Using Logarithmic Laws, Please :)

• Mar 6th 2009, 12:04 AM
Help With Transpositon Involving Using Logarithmic Laws, Please :)
hello there everyone,

there is a formula that i have learnt for my job and am having a little trouble trying to make another character the subject of the equation.

here is the equation/formula that i have drawn :

http://i608.photobucket.com/albums/t...Logarithms.jpg

as you can see, i am trying to make the top character "t" the subject of my formula but am having trouble doing so. i can use simple transposition to do some of it but am stuck at the end when i have to use logarithmic laws to separate the "+/- t" from the "- e" and "+/-T ".

i have done a little work with logarithms in school but it has been a while and haven't found any great help on the internet to help me with doing this myself. if its also not too much trouble, i'd love it if you could show me how it is done or how to do it so that i know for future reference how to tackle such a question again haha (Nod).

if anyone could find the time to help me, i would be ever so grateful (Nod).

thanks everyone, greatly appreciate it !!

PS: sorry for the nods; i couldn't find smiley faces haha
• Mar 6th 2009, 04:56 AM
Jester
:)
Quote:

hello there everyone,

there is a formula that i have learnt for my job and am having a little trouble trying to make another character the subject of the equation.

here is the equation/formula that i have drawn :

http://i608.photobucket.com/albums/t...Logarithms.jpg

as you can see, i am trying to make the top character "t" the subject of my formula but am having trouble doing so. i can use simple transposition to do some of it but am stuck at the end when i have to use logarithmic laws to separate the "+/- t" from the "- e" and "+/-T ".

i have done a little work with logarithms in school but it has been a while and haven't found any great help on the internet to help me with doing this myself. if its also not too much trouble, i'd love it if you could show me how it is done or how to do it so that i know for future reference how to tackle such a question again haha (Nod).

if anyone could find the time to help me, i would be ever so grateful (Nod).

thanks everyone, greatly appreciate it !!

PS: sorry for the nods; i couldn't find smiley faces haha

$\displaystyle V = V_s\left(1 - e^{-t/ \tau}\right)$
$\displaystyle \frac{V}{V_s} = 1 - e^{-t/ \tau}$
$\displaystyle e^{-t/ \tau} = 1 - \frac{V}{V_s}$
$\displaystyle \ln e^{-t/ \tau} = \ln \left| 1 - \frac{V}{V_s} \right|$
$\displaystyle -\frac{t}{ \tau} = \ln \left| 1 - \frac{V}{V_s} \right|$
$\displaystyle t = - \tau \ln \left| 1 - \frac{V}{V_s} \right|$
:) (after more)
• Mar 7th 2009, 06:50 PM