Expand the Logarithmic Expression log of (cd^2)/(fg)

$\log (\frac{c d^{2}}{f g})$

Rewrite $\log (\frac{c d^{2}}{f g})$ as $\log (c d^{2}) - \log (f g)$ .

$\log (c d^{2}) - \log (f g)$

Rewrite $\log (c d^{2})$ as $\log (c) + \log (d^{2})$ .

$\log (c) + \log (d^{2}) - \log (f g)$

Expand $\log (d^{2})$ by moving $2$ outside the logarithm.

$\log (c) + 2 \log (d) - \log (f g)$

Rewrite $\log (f g)$ as $\log (f) + \log (g)$ .

$\log (c) + 2 \log (d) - (\log (f) + \log (g))$

Apply the distributive property.

$\log (c) + 2 \log (d) - \log (f) - \log (g)$