Precalculus Examples

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

Step 1

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

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

Step 2

Expand $\log_{b} (3^{5})$ by moving $5$ outside the logarithm.

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

Step 3

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

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