Precalculus Examples

$3 \log_{8} (2) + 3 \log_{8} (x) + 15 \log_{8} (y)$

Step 1

Simplify each term.

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Step 1.1

Logarithm base $8$ of $2$ is $\frac{1}{3}$ .

$3 (\frac{1}{3}) + 3 \log_{8} (x) + 15 \log_{8} (y)$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Cancel the common factor.

$3 (\frac{1}{3}) + 3 \log_{8} (x) + 15 \log_{8} (y)$

Step 1.2.2

Rewrite the expression.

$1 + 3 \log_{8} (x) + 15 \log_{8} (y)$

Step 1.3

Simplify $3 \log_{8} (x)$ by moving $3$ inside the logarithm.

$1 + \log_{8} (x^{3}) + 15 \log_{8} (y)$

Step 1.4

Simplify $15 \log_{8} (y)$ by moving $15$ inside the logarithm.

$1 + \log_{8} (x^{3}) + \log_{8} (y^{15})$

Step 2

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

$1 + \log_{8} (x^{3} y^{15})$