Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.5 Exponential and Logarithmic Equations - 4.5 Exercises - Page 470: 91

$t=-\frac{2}{R}ln(1- \frac{IR}{E})$

$I=\frac{E}{R}(1-e^{-Rt/2}) \longrightarrow 1-e^{-Rt/2} = \frac{IR}{E} \longrightarrow e^{-Rt/2}=1- \frac{IR}{E} \longrightarrow -\frac{Rt}{2}=ln(1- \frac{IR}{E})\longrightarrow t=-\frac{2}{R}ln(1- \frac{IR}{E})$