1. ## basic logarithm question

How do you get that lower equation from the upper one?

2. Hi

Take the natural log of the upper equation

$\displaystyle \ln \left(e^{-kt}\right) = \ln \frac12$

ln being the inverse function of exp, $\displaystyle \ln(e^x) = x$

The equation becomes

$\displaystyle -kt = \ln \frac12$

3. thanks.

4. Also $\displaystyle \ln \left(\frac{1}{2}\right) = \ln (2^{-1}) = -\ln(2)$

So $\displaystyle kt = \ln(2)$ which is a more usual form in exponential decay