Expand the Logarithmic Expression log of (a^2b^3)/(c^4)

$\log (\frac{a^{2} b^{3}}{c^{4}})$

Rewrite $\log (\frac{a^{2} b^{3}}{c^{4}})$ as $\log (a^{2} b^{3}) - \log (c^{4})$ .

$\log (a^{2} b^{3}) - \log (c^{4})$

Expand $\log (c^{4})$ by moving $4$ outside the logarithm.

$\log (a^{2} b^{3}) - (4 \log (c))$

Multiply $4$ by $- 1$ .

$\log (a^{2} b^{3}) - 4 \log (c)$

Rewrite $\log (a^{2} b^{3})$ as $\log (a^{2}) + \log (b^{3})$ .

$\log (a^{2}) + \log (b^{3}) - 4 \log (c)$

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

$2 \log (a) + \log (b^{3}) - 4 \log (c)$

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

$2 \log (a) + 3 \log (b) - 4 \log (c)$