Precalculus Examples

$\log_{b} (45)$

Step 1

Rewrite $\log_{b} (45)$ as $\log_{b} (3^{2} \cdot 5)$ .

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

Step 2

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

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

Step 3

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

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