Expand the Logarithmic Expression log of 10m^4n^-2

$\log (10 m^{4} n^{- 2})$

Rewrite $\log (10 m^{4} n^{- 2})$ as $\log (10 m^{4}) + \log (n^{- 2})$ .

$\log (10 m^{4}) + \log (n^{- 2})$

Rewrite $\log (10 m^{4})$ as $\log (10) + \log (m^{4})$ .

$\log (10) + \log (m^{4}) + \log (n^{- 2})$

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

$\log (10) + 4 \log (m) + \log (n^{- 2})$

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

$\log (10) + 4 \log (m) - 2 \log (n)$

Logarithm base $10$ of $10$ is $1$ .

$1 + 4 \log (m) - 2 \log (n)$