\(\begin{aligned}i & =\frac{U}{R}\cdot(1-e^{-\frac{t}{\tau}}) & & |\,\cdot\frac{R}{U}\\\frac{iR}{U} & =1-e^{-\frac{t}{\tau}} & & |\,-1\\\frac{iR}{U}-1 & =-e^{-\frac{t}{\tau}} & & |\,\cdot(-1)\\1-\frac{iR}{U} & =e^{-\frac{t}{\tau}} & & |\,\ln\\\ln\left(1-\frac{iR}{U}\right) & =-\frac{1}{\tau} & & |\,\cdot\tau\\\tau\cdot\ln\left(1-\frac{iR}{U}\right) & =-1 & & |\,:\ln\left(1-\frac{iR}{U}\right)\\\tau & =-\frac{1}{\ln\left(1-\frac{iR}{U}\right)}\end{aligned}\)