Expand the Logarithmic Expression log base 2 of 40

$\log_{2} (40)$

Rewrite $\log_{2} (40)$ as $\log_{2} (2^{3} \cdot 5)$ .

$\log_{2} (2^{3} \cdot 5)$

Rewrite $\log_{2} (2^{3} \cdot 5)$ as $\log_{2} (2^{3}) + \log_{2} (5)$ .

$\log_{2} (2^{3}) + \log_{2} (5)$

Use logarithm rules to move $3$ out of the exponent.

$3 \log_{2} (2) + \log_{2} (5)$

Logarithm base $2$ of $2$ is $1$ .

$3 \cdot 1 + \log_{2} (5)$

Multiply $3$ by $1$ .

$3 + \log_{2} (5)$