Question

O módulo da raiz da equação log6 (2x + 5)-log6 (32x+ 20) = -1 é
a) 2
b) 1
c) 1/2
d) 3/4
e) 2/5​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_6\:(2x + 5) - log_6\:(32x + 20) = -1}$

$\mathsf{log_6\:(2x + 5) - log_6\:(32x + 20) = log_6\:6^{-1}}$

$\mathsf{log_6\:\dfrac{2x + 5}{32x + 20} = log_6\:6^{-1}}$

$\mathsf{\dfrac{2x + 5}{32x + 20} = \dfrac{1}{6}}$

$\mathsf{12x + 30 = 32x + 20}$

$\mathsf{32x - 12x = 30 - 20}$

$\mathsf{20x = 10}$

$\boxed{\boxed{\mathsf{x = \dfrac{1}{2}}}}\leftarrow\textsf{letra C}$