Answer
$\log_5 3$ + 2$\log_5 x$ - 3$\log_5 y$
Work Step by Step
$Expand$ $the$ $expression$:
$\log_5 \frac{3x^2}{y^3}$
Apply the Second Law of Logarithms
$\log_5 \frac{3x^2}{y^3}$ = $\log_5 3x^2$ - $\log_5 y^3$
Apply the First Law of Logarithms to $\log_5 3x^2$
$\log_5 (3\times x^2)$ = $\log_5 3$ + $\log_5 x^2$
$\log_5 3x^2$ - $\log_5 y^3$ = $\log_5 3$ + $\log_5 x^2$ - $\log_5 y^3$
Apply the Third Law of logarithms to $\log_5 x^2$ and $\log_5 y^3$
$\log_5 x^2$ = 2$\log_5 x$
$\log_5 y^3$ = 3$\log_5 y$
$\log_5 3$ + $\log_5 x^2$ - $\log_5 y^3$ = $\log_5 3$ + 2$\log_5 x$ - 3$\log_5 y$
