Question

(CEPBJ) O par ordenado (x,y) é solução do sistema a seguir.
log3x+log3y=7
log3y-log3x=3
Então, se K = y − x, o valor de K é igual a: a. 234.
b. 720.
c. 240.
d. 162.
e. 243.

Answer 1

$\left \{ {{\log_3x+\log_3y=7} \atop {\log_3y-\log_3x=3}} \right. \\\\ \log_3x+\log_3y=7\\\log_3(xy)=7\\3^7=xy\\xy=2187\\\\\log_3y-\log_3x=3\\\log_3\left(\dfrac{y}{x}\right)=3\\\\\dfrac{y}{x}=3^3\\\\y=27x\\\\\\x(27x)=2187\\27x^2=2187\\x^2=81\\x=9\\\\y=243\\\\y-x=243-81=162$