Expand the Logarithmic Expression log of (2xy)/(3z^3)

$\log (\frac{2 x y}{3 z^{3}})$

Rewrite $\log (\frac{2 x y}{3 z^{3}})$ as $\log (2 x y) - \log (3 z^{3})$ .

$\log (2 x y) - \log (3 z^{3})$

Rewrite $\log (2 x y)$ as $\log (2 x) + \log (y)$ .

$\log (2 x) + \log (y) - \log (3 z^{3})$

Rewrite $\log (2 x)$ as $\log (2) + \log (x)$ .

$\log (2) + \log (x) + \log (y) - \log (3 z^{3})$

Rewrite $\log (3 z^{3})$ as $\log (3) + \log (z^{3})$ .

$\log (2) + \log (x) + \log (y) - (\log (3) + \log (z^{3}))$

Expand $\log (z^{3})$ by moving $3$ outside the logarithm.

$\log (2) + \log (x) + \log (y) - (\log (3) + 3 \log (z))$

Simplify each term.

Apply the distributive property.

$\log (2) + \log (x) + \log (y) - \log (3) - (3 \log (z))$

Multiply $3$ by $- 1$ .

$\log (2) + \log (x) + \log (y) - \log (3) - 3 \log (z)$