Solve for x: 4^x = 8^x-1.

Write both sides with a common base of $2$: $4^x=(2^2)^x=2^{2x}$ and $8^{x-1}=(2^3)^{x-1}=2^{3x-3}$. Equal bases mean equal exponents, so $2x=3x-3$, which gives $x=3$, choice D. Check: $4^3=64$ and $8^{2}=64$. Choice A ($x=1$) gives $4$ and $1$. Choice B ($x=2$) gives $16$ and $8$. Choice C ($x=-3$) makes the equation $2x=3x-3$ fail; it comes from a sign mistake when moving $3x$. The common-base method turns an exponential equation into a linear one.