 In this video, we provide the solution to question number 12 for the practice final exam for math 1050. We have to solve the exponential equation 2 raised to the 2x minus 8 power is equal to 2 raised to the 5x plus 1 power. Now, as exponential functions are 1 to 1, if you ever have the expression that a to the m equals a to the n, you can essentially just cancel out the bases and you end up with m is equal to n. So if 2x exponential expressions of the same base are equal, it must be that their exponents are equal. So since both sides of this equation involve a power of 2, we can actually remove the 2 from play and just set the exponents equal to each other. So this becomes 2x minus 8 is equal to 5x plus 1. Solving this equation, I'm going to subtract 2x from both sides. I'm going to subtract 1 from both sides. We end up with on the left hand side, negative 8 minus 1 is a negative 9. On the right hand side, 5x minus 2x is a 3x. So we want to divide both sides by 3 and we end up with x being equal to negative 3. So we see that the correct answer would be choice F.