Precalculus Examples

$\log_{2} (4^{2} \cdot 3^{4})$

Step 1

Rewrite $\log_{2} (4^{2} \cdot 3^{4})$ as $\log_{2} (4^{2}) + \log_{2} (3^{4})$ .

$\log_{2} (4^{2}) + \log_{2} (3^{4})$

Step 2

Expand $\log_{2} (4^{2})$ by moving $2$ outside the logarithm.

$2 \log_{2} (4) + \log_{2} (3^{4})$

Step 3

Expand $\log_{2} (3^{4})$ by moving $4$ outside the logarithm.

$2 \log_{2} (4) + 4 \log_{2} (3)$

Step 4

Logarithm base $2$ of $4$ is $2$ .

$2 \cdot 2 + 4 \log_{2} (3)$

Step 5

Multiply $2$ by $2$ .

$4 + 4 \log_{2} (3)$