TITLE: Why does this ln function inverse?
QUESTION [5 upvotes]: I'm going through applications of separable equations and came across an example of half-lives:
$$M(t)=\frac{M}{2}=Me^{-kt}$$
Factoring out $M$, $\frac{1}{2}=e^{-kt}$.
To solve for $t$, $\ln\left(\frac{1}{2}\right)=-kt$.
And then the answer is $t=\frac1k{\ln 2}$.
Why isn't the value for $t=-\frac1k{\ln \frac12}$?
Thanks:)

REPLY [3 votes]: $\ln{\frac{1}{2}} = \ln{1} - \ln{2} = 0 - \ln{2} = -\ln{2}$