 In this video, we provide the solution to question number two for practice exam number four for math 1050 And we have to solve the exponential equation 9 raised to the negative x plus 15 power is equal to 27 to the x power Now we can try to solve this equation using logarithms But it's much easier to observe that the bases in play here 9 and 27 are both Powers of 3 so using some exponential laws we can make life a lot easier for us on the left hand side We have 3 squared because that's 9 to the negative x plus 15 And so as you have an exponent now raised to an exponent We can multiply them together and the left hand side becomes 3 to the negative 2x plus 30 power Similarly on the right hand side 27 is the same thing as 3 cubed you raise this to the x so multiplying the exponents together We get 3 to the x power So now we have 3 to the negative 2x plus 30 power and that's equal to 3 to the 3x power Since the bases are now the same we can cancel out the base and thus get the linear equation negative 2x plus 30 is Equal to 3x I'm going to add 2x to both sides This gives me 30 is equal to 5x and then I'm going to divide both sides by 5 Thus giving me x equals 30 over 5 aka 6 And therefore we see the correct answer is then D