Chapter 5 - Logarithmic Functions - 5.1 Logarithms and Their Properties - Exercises and Problems for Section 5.1 - Exercises and Problems - Page 195: 68

11.2

Using the properties of logarithms, we find: $$\ln \left(400e^{0.1x}\right)=\ln \left(500e^{0.08x}\right) \\ \ln \left(400\right)+\ln \left(e^{0.1x}\right)=\ln \left(500\right)+\ln \left(e^{0.08x}\right) \\ \ln \left(400\right)+\ln \left(e^{0.1x}\right)=\ln \left(500\right)+\ln \left(e^{0.08x}\right) \\ x=\frac{100\ln \left(5\right)-200\ln \left(2\right)}{2} \\ x=11.2$$