Exponential Decay of a radioactive substance If $375$ mg of a radioactive substance decays to $300$ mg in $72$ hours, find the 
half-life of the element. I first used the mathematical formula of 
$$A = A_0e^{kt}$$ 
or exponential decay. After doing my calculations with natural logarithms, I got 
an odd answer of $1.3$ days, by dividing $\ln (375)/\ln (72)$. I know this cannot be the half-life of a radioactive element. Where is my wrong step?

Because it is exponential decay, I would prefer to use $A(t)=A(0)e^{-kt}$. 
Then $\frac{300}{375}=e^{-72k}$, so $k=\frac{1}{72}\ln(375/300)$. 
Now for the half-life $\tau$, we have $\frac{1}{2}A(0)=A(0)e^{-k\tau}$, so $k\tau=\ln 2$. It follows that the half-life, in hours, is $72\frac{\ln 2}{\ln(375/300)}$.
