The expanded form of  $\log \frac{343}{125}$ is

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

$\log \frac{343}{125}=\log 343-\log 125$

$=\log 7^3-\log 5^3$

${\log }_a{x}^m=m{\log }_{a}x=3\log 7-3\log 5$

$\log \frac{343}{125}=3(\log 7-\log 5)$