Question

resolva o sistema:
log x-log y =log 2 4x-y=16

Answer 1

$\large\boxed{\begin{array}{l}\sf\ell ogx-\ell ogy=\ell og2\\\sf \ell og\bigg(\dfrac{x}{y}\bigg)=\ell og2\\\sf \dfrac{x}{y}=2\implies x=2y\\\begin{cases}\sf\ell ogx-\ell ogy=\ell og2\\\sf 4x-y=16\end{cases}\\\\\begin{cases}\sf x=2y\\\sf4x-y=16\end{cases}\\\sf 4\cdot2y-y=16\\\sf 7y=16\\\\\sf y=\dfrac{16}{7}\\\\\sf x=2y\\\sf x=2\cdot\dfrac{16}{7}\\\\\sf x=\dfrac{32}{7}\\\\\sf S=\bigg\{\dfrac{32}{7},\dfrac{16}{7}\bigg\}\end{array}}$