How can I solve for $m$ in this equation, where $e$ is Euler's number, and $p,k,m \gt 0$, and $p \lt 1$?
$p = \left(1 - e^{\frac{-kn}{m}}\right)^k$
How can I solve for $m$ in this equation, where $e$ is Euler's number, and $p,k,m \gt 0$, and $p \lt 1$?
$p = \left(1 - e^{\frac{-kn}{m}}\right)^k$
$1 - e^{\frac{-kn}{m}} = \sqrt[k]{p} \Rightarrow e^{\frac{-kn}{m}} =1-\sqrt[k]{p} \Rightarrow \frac{-kn}{m}=\ln (1-\sqrt[k]{p}) \Rightarrow $
$m= \frac{-kn}{\ln (1-\sqrt[k]{p})}$