Precalculus Examples

$\log_{b} (3 b^{4})$

Step 1

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

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

Step 2

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

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

Step 3

Logarithm base $b$ of $b$ is $1$ .

$\log_{b} (3) + 4 \cdot 1$

Step 4

Multiply $4$ by $1$ .

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