solve: 2^2x=8^x-1 for x
\(2^{2x}=8^{x-1}\\\\2^{2x}=(2^3)^{x-1}\\\\2^{2x}=2^{3(x-1)}\iff2x=3(x-1)\\\\2x=3x-3\ \ \ |subtract\ 3x\ from\ both\ sides\\\\-x=-3\ \ \ |change\ the\ signs\\\\\boxed{x=3}\)
