Expand the Logarithmic Expression log base 5 of 20

$\log_{5} (20)$

Rewrite $\log_{5} (20)$ as $\log_{5} (2^{2} \cdot 5)$ .

$\log_{5} (2^{2} \cdot 5)$

Rewrite $\log_{5} (2^{2} \cdot 5)$ as $\log_{5} (2^{2}) + \log_{5} (5)$ .

$\log_{5} (2^{2}) + \log_{5} (5)$

Simplify each term.

Expand $\log_{5} (2^{2})$ by moving $2$ outside the logarithm.

$2 \log_{5} (2) + \log_{5} (5)$

Logarithm base $5$ of $5$ is $1$ .

$2 \log_{5} (2) + 1$