Expand the Logarithmic Expression log base 7 of 7mn^4

$\log_{7} (7 m n^{4})$

Rewrite $\log_{7} (7 m n^{4})$ as $\log_{7} (7 m) + \log_{7} (n^{4})$ .

$\log_{7} (7 m) + \log_{7} (n^{4})$

Rewrite $\log_{7} (7 m)$ as $\log_{7} (7) + \log_{7} (m)$ .

$\log_{7} (7) + \log_{7} (m) + \log_{7} (n^{4})$

Expand $\log_{7} (n^{4})$ by moving $4$ outside the logarithm.

$\log_{7} (7) + \log_{7} (m) + 4 \log_{7} (n)$

Logarithm base $7$ of $7$ is $1$ .

$1 + \log_{7} (m) + 4 \log_{7} (n)$