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Math Help - Solving for e

  1. #1
    Junior Member
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    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.
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  2. #2
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    Quote Originally Posted by mark090480 View Post
    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
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