Question

Se o quociente de $64^{x-1}$ por $4^{x-1}$ é $256^{2x}$ , quanto é x ?

Answer 1

$\dfrac{64^{x-1}}{4^{x-1}} = 256^{2x} \\ \\ 64^{x-1} \cdot 4^{x-1} = 256^{2x} \\ \\ (2^6)^{x-1} \cdot (2^2)^{x-1} = (2^8)^{2x} \\ \\ 2^{6x-6} \cdot2^{2x-2} = 2^{16x} \\ \\ 2^{6x-6 + 2x - 2} = 2^{16x} \\ \\ \not2^{8x-8} = \not2^{16x} \\ \\ 8x - 8 = 16 x \\ \\8x = -8 \\ \\ \boxed{x = -1}$