# Math Help - Solving for e

1. ## Solving for e

Hi

How do I make t the subject in this equation? I have problems with the e.

V=Vo e^-t/c

I did this:

ln(v) = Vo -t/c

c ln(v) = Vo - t

-c ln(v)/Vo = t

However this does not work. Where did I go wrong?

Thanks.

2. Originally Posted by mark090480
Hi

How do I make t the subject in this equation? I have problems with the e.

V=Vo e^-t/c

I did this:

ln(v) = Vo -t/c

c ln(v) = Vo - t

-c ln(v)/Vo = t

However this does not work. Where did I go wrong?

Thanks.
$\displaystyle v=v_0e^{-\frac{t}{c}} \iff \frac{v}{v_0}=e^{-\frac{t}{c}}$

Now taking the natural log of both sides gives

$\displaystyle \ln\left( \frac{v}{v_0}\right)=-\frac{t}{c} \iff -c\ln\left( \frac{v}{v_0}\right)=t$