Expand the Logarithmic Expression log base 7 of 42

$\log_{7} (42)$

Rewrite $\log_{7} (42)$ as $\log_{7} (2 \cdot 3 \cdot 7)$ .

$\log_{7} (2 \cdot 3 \cdot 7)$

Rewrite $\log_{7} (2 \cdot 3 \cdot 7)$ as $\log_{7} (2 \cdot 3) + \log_{7} (7)$ .

$\log_{7} (2 \cdot 3) + \log_{7} (7)$

Simplify each term.

Rewrite $\log_{7} (2 \cdot 3)$ as $\log_{7} (2) + \log_{7} (3)$ .

$\log_{7} (2) + \log_{7} (3) + \log_{7} (7)$

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

$\log_{7} (2) + \log_{7} (3) + 1$