Cho ${\log }_{3}5=a$, ${\log }_{3}10=b$ và ${\log }_{\sqrt{3}}50=ma+nb$. Mệnh đề nào sau đây đúng?

$\log x+\log y=\log (xy)$.

$\log (x+y)=\log x+\log y$.

$\log \sqrt{xy}=\frac{1}{2}(\log x+\log y)$.

$\log \frac{x}{y}=\log x-\log y$.

$-9$.

$8$.

$25$.

$-10$.

$5{\log }_{a}b$.

$\frac{1}{5}+{\log }_{a}b$.

$5+{\log }_{a}b$.

$\frac{1}{5}{\log }_{a}b$.

log 10 x2 = 1 + log x .

log (10 x 2 ) = 1 + 2log x .

log (10 x ) = 10 + 2log x .
2
( )

log 10 x 2 = 2 + log x .

$1$.

$4$.

$5$.

$6$.

${\log }_a\frac{x}{y}={\log }_{a}x-{\log }_{a}y$.

${\log }_a\frac{x}{y}=\frac{{\log }_{a}x}{{\log }_{a}y}$.

${\log }_a\frac{x}{y}={\log }_{a}x+{\log }_{a}y$.

${\log }_a\frac{x}{y}={\log }_a(x-y)$.