Precalculus Examples

$3 \log_{8} (4) + \log_{8} (4) + \log_{8} (2)$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$3 \log_{8} (4) + \log_{8} (4 \cdot 2)$

Step 2

Simplify each term.

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Step 2.1

Logarithm base $8$ of $4$ is $\frac{2}{3}$ .

$3 (\frac{2}{3}) + \log_{8} (4 \cdot 2)$

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Cancel the common factor.

$3 (\frac{2}{3}) + \log_{8} (4 \cdot 2)$

Step 2.2.2

Rewrite the expression.

$2 + \log_{8} (4 \cdot 2)$

Step 2.3

Multiply $4$ by $2$ .

$2 + \log_{8} (8)$

Step 2.4

Logarithm base $8$ of $8$ is $1$ .

$2 + 1$

Step 3

Add $2$ and $1$ .

$3$