Precalculus Examples

$5 \log_{5} (12)$

Step 1

Rewrite $\log_{5} (12)$ as $\log_{5} (2^{2} \cdot 3)$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $2$ by $5$ .

$10 \log_{5} (2) + 5 \log_{5} (3)$