Answer
$\log_5 (\frac{x^2y^4}{z^6})$
Work Step by Step
$Combine$ $the$ $expression$:
$2$$($$\log_5 x$ + $2$$\log_5 y$ - $3$$\log_5 z$$)$
Distribute the 2 to all variables in the parenthesis
$2$$\log_5 x$ + $2$$\times$$2$$\log_5 y$ - $2$$\times$$3$$\log_5 z$
$2$$\log_5 x$ + $4$$\log_5 y$ - $6$$\log_5 z$
Apply the Third Law of Logarithms for $2$$\log_5 x$, $4$$\log_5 y$, and $6$$\log_5 z$
$2$$\log_5 x$ = $\log_5 x^2$
$4$$\log_5 y$ = $\log_5 y^4$
$6$$\log_5 z$ = $\log_5 x^6$
$\log_5 x^2$ + $\log_5 y^4$ - $\log_5 z^6$
Apply the First Law of Logarithms for $\log_5 x^2$ + $\log_5 y^4$
$\log_5 x^2$ + $\log_5 y^4$ = $\log_5 (x^2\times y^4)$
$\log_5 (x^2y^4)$ - $\log_5 z^6$
Apply the Second Law of Logarithms
$\log_5 (x^2y^4)$ - $\log_5 z^6$ = $\log_5 (\frac{x^2y^4}{z^6})$
