What value of x satisfies 4^x-1 = 8^x+2?

Rewrite both sides with base 2: $4 = 2^2$ and $8 = 2^3$, so $2^{2(x-1)} = 2^{3(x+2)}$. Equal bases mean equal exponents: $2x - 2 = 3x + 6$. Subtract $2x$ and 6: $-8 = x$, choice C. Check: $4^{-9} = 2^{-18}$ and $8^{-6} = 2^{-18}$. Choices A ($-1$), B (1), and D (2) fail the check: for $x = 1$, $4^0 = 1$ but $8^3 = 512$. Typical errors are forgetting to distribute the 2 and 3 across the parentheses or moving the constants with the wrong sign.