If \(3^x = 27^{y - 5}\) and \(2^y = 8^{2x - 4}\), then find y - x.
Note that \(27=3^3 \text{ and } 8=2^3\)
So \(3^x = 3^{3(y-5)} \text{ and }2^y=2^{3(2x-4)}\)
Now equate powers so that you have two equations for x and y:
x = 3(y - 5) and y = 3(2x - 4)
Can you take it from here?
