Chapter 5 - Logarithmic Functions - 5.1 Logarithms and Their Properties - Exercises and Problems for Section 5.1 - Exercises and Problems - Page 195: 63

-9.95

Using the properties of logarithms, we find: $$\ln \left(e^{x+5}\right)=\ln \left(7\cdot \:2^x\right) \\ \left(x+5\right)\ln \left(e\right)=\ln \left(7\right)+x\ln \left(2\right) \\ x+5=\ln \left(7\right)+x\ln \left(2\right) \\ x=\frac{\ln \left(7\right)-5}{1-\ln \left(2\right)} \\ x=-9.95$$