 In this video we provide the solution to question number six for practice exam four for math 1050 we have to solve the equation the logarithm of e to the negative 2x is equal to eight. Well we have logarithms we have exponentials we use the properties we've learned about logs and exponentials to help us out here. The first thing to observe is that the natural log and the natural exponential are inverses functions. So if I take the natural log of e to the negative 2x I'm asking what power of e will give you e to the negative 2x power. The answer is in the question the natural log and e cancel out and this equation just becomes negative 2x is equal to eight. Divide both sides by negative two we then see the correct answer would then be x equals negative four thus we get choice e.