Precalculus Examples

$3 \log_{8} (y) - \frac{1}{4} \cdot \log_{8} (x) + 2 \log_{8} (w)$

Step 1

Simplify each term.

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Step 1.1

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

$\log_{8} (y^{3}) - \frac{1}{4} \cdot \log_{8} (x) + 2 \log_{8} (w)$

Step 1.2

Multiply $- \frac{1}{4} \log_{8} (x)$ .

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Step 1.2.1

Reorder $\log_{8} (x)$ and $\frac{1}{4}$ .

$\log_{8} (y^{3}) - (\frac{1}{4} \log_{8} (x)) + 2 \log_{8} (w)$

Step 1.2.2

Simplify $\frac{1}{4} \log_{8} (x)$ by moving $\frac{1}{4}$ inside the logarithm.

$\log_{8} (y^{3}) - \log_{8} (x^{\frac{1}{4}}) + 2 \log_{8} (w)$

Step 1.3

Simplify $2 \log_{8} (w)$ by moving $2$ inside the logarithm.

$\log_{8} (y^{3}) - \log_{8} (x^{\frac{1}{4}}) + \log_{8} (w^{2})$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{8} (\frac{y^{3}}{x^{\frac{1}{4}}}) + \log_{8} (w^{2})$

Step 3

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

$\log_{8} (\frac{y^{3}}{x^{\frac{1}{4}}} w^{2})$

Step 4

Combine $\frac{y^{3}}{x^{\frac{1}{4}}}$ and $w^{2}$ .

$\log_{8} (\frac{y^{3} w^{2}}{x^{\frac{1}{4}}})$