Answer
3$\log x$ + 4$\log y$ - 6$\log z$
Work Step by Step
$Expand$ $the$ $expression$:
$\log \frac{x^3y^4}{z^6}$
Apply the Second Law of Logarithms
$\log \frac{x^3y^4}{z^6}$ = $\log {x^3y^4}$ - $\log z^6$
Apply the First Law of Logarithms for $\log {x^3y^4}$
$\log {(x^3\times y^4)}$ = $\log x^3$ + $\log y^4$
$\log x^3$ + $\log y^4$ - $\log z^6$
Apply the Third Law of Logarithms for $\log x^3$, $\log y^4$, and $\log z^6$
$\log x^3$ = 3$\log x$
$\log y^4$ = 4$\log y$
$\log z^6$ = 6$\log z$
Assemble the expression
3$\log x$ + 4$\log y$ - 6$\log z$