# Math Help - solving pharmacokinetic equation

1. ## solving pharmacokinetic equation

Hi,

I'm having trouble transforming the following equation to predict ka (absorption rate constant):

tmax = ln(ka/k)/(ka-k)

So far I've tried (not sure if correct):

tmax = ln(ka) -ln(k)/(ka-k)
tmax(ka -k) -ln(ka) = -ln(k)
tmax.ka - tmax.k - ln(ka) = -ln(k)
tmax.ka - ln(ka) = -ln(k)+tmax.k

2. Originally Posted by kdt
Hi,

I'm having trouble transforming the following equation to predict ka (absorption rate constant):

tmax = ln(ka/k)/(ka-k)

So far I've tried (not sure if correct):

tmax = ln(ka) -ln(k)/(ka-k)
tmax(ka -k) -ln(ka) = -ln(k)
tmax.ka - tmax.k - ln(ka) = -ln(k)
tmax.ka - ln(ka) = -ln(k)+tmax.k

You have $\displaystyle t_{max} = \frac{\ln(k_a) - \ln(k)}{k_a - k}$. This equation cannot be solved for $k_a$ without introducing a special function.
What you should do is collect data, model the curve from the data and then estimate the value of $k_a$.