Precalculus Examples

$\log_{b} (216 b)$

Step 1

Rewrite $\log_{b} (216 b)$ as $\log_{b} (216) + \log_{b} (b)$ .

$\log_{b} (216) + \log_{b} (b)$

Step 2

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

$\log_{b} (216) + 1$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{b} (216)$ as $\log_{b} (2^{3} \cdot 3^{3})$ .

$\log_{b} (2^{3} \cdot 3^{3}) + 1$

Step 3.2

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

$\log_{b} (2^{3}) + \log_{b} (3^{3}) + 1$

Step 3.3

Simplify each term.

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Step 3.3.1

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

$3 \log_{b} (2) + \log_{b} (3^{3}) + 1$

Step 3.3.2

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

$3 \log_{b} (2) + 3 \log_{b} (3) + 1$