Precalculus Examples

$\log_{2} (5^{2} \cdot 4^{5})$

Step 1

Rewrite $\log_{2} (5^{2} \cdot 4^{5})$ as $\log_{2} (5^{2}) + \log_{2} (4^{5})$ .

$\log_{2} (5^{2}) + \log_{2} (4^{5})$

Step 2

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

$2 \log_{2} (5) + \log_{2} (4^{5})$

Step 3

Expand $\log_{2} (4^{5})$ by moving $5$ outside the logarithm.

$2 \log_{2} (5) + 5 \log_{2} (4)$

Step 4

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

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

Step 5

Multiply $5$ by $2$ .

$2 \log_{2} (5) + 10$