Chapter 5 - Logarithmic Functions - 5.1 Logarithms and Their Properties - Exercises and Problems for Section 5.1 - Exercises and Problems - Page 195: 59

6.02

Using the properties of logarithms, we find: $$e^{-0.2t}=\frac{3}{10} \\ \ln \left(e^{-0.2t}\right)=\ln \left(\frac{3}{10}\right) \\ -0.2t=\ln \left(\frac{3}{10}\right) \\ t=-5\ln \left(\frac{3}{10}\right) \\ t=6.02$$