Question

(AJUDA) EQUAÇÃO EXPONENCIAL

A) 64^3x-1=8
B) 8^3x+4.4^2x-1=16^x+1

Answer 1

a)

$64^{3x-1} = 8 \\ \\ (8^2)^{3x-1} = 8 \\ \\ 8^{6x - 2} = 8 \\ \\ 6x - 2 = 1 \\ 6x = 3 \\ \\ x = \frac{3}{6} \\ \\ x = \frac{1}{2}$


b)

$8^{3x + 4}\,.\,4^{2x-1}=16^{x+1} \\ \\ (2^3)^{3x + 4} \,.\,(2^2)^{2x - 1} = (2^4)^{x+1} \\ \\ 2^{9x + 12}\,.\,2^{4x - 2} = 2^{4x + 4} \\ \\ 2^{9x + 12 + 4x - 2} = 2^{4x+4} \\ \\ 2^{13x + 10} = 2^{4x+4} \\ \\ 13x + 10 = 4x + 4 \\ \\ 13x - 4x = 4 - 10 \\ \\ 9x = -6 \\ \\ x = -\frac{6}{9}$