Question

Resolvendo a equação exponencial 16^2X = 64^4X-3, encontramos como solução:a)X = 3/4b)X = 9/8c)X = 1/2d)X = 5/7e)X = 7/9

Answer 1

Olá!

$\\ \mathsf{16^{2x} = 64^{4x - 3}} \\\\ \mathsf{(4^2)^{2x} = (4^3)^{4x - 3}} \\\\ \mathsf{4^{2 \cdot 2x} = 4^{3 \cdot (4x - 3)}} \\\\ \mathsf{4^{4x} = 4^{12x - 9}}$

 Comparando os expoentes, já que as bases são iguais, temos que:

$\\ \mathsf{4x = 12x - 9} \\\\ \mathsf{4x - 12x = - 9} \\\\ \mathsf{- 8x = - 9} \\\\ \mathsf{x = \frac{- 9}{- 8}} \\\\ \boxed{\mathsf{x = \frac{9}{8}}}$