Precalculus Examples

$\log_{2} (20)$

Step 1

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

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

Step 2

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

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

Step 3

Use logarithm rules to move $2$ out of the exponent.

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

Step 4

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

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

Step 5

Multiply $2$ by $1$ .

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