Answer
$log_{7}y+3log_{7}z-log_{7}x$
Work Step by Step
The quotient property of logarithms tells us that $log_{b}\frac{x}{y}=log_{b}x-log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$).
Therefore, $log_{7}\frac{yz^{3}}{x}=log_{7}(yz^{3})-log_{7}x$.
The product property of logarithms tells us that $log_{b}xy=log_{b}x+log_{b}y$ (where x, y, and, b are positive real numbers and $b\ne1$).
Therefore, $log_{7}(yz^{3})-log_{7}x=log_{7}y+log_{7}z^{3}-log_{7}x$.
The power property of logarithms tells us that $log_{b}x^{r}=r log_{b}x$ (where x and b are positive real numbers, $b\ne1$, and r is a real number).
Therefore, $log_{7}y+log_{7}z^{3}-log_{7}x=log_{7}y+3log_{7}z-log_{7}x$
