Precalculus Examples

$3 \log_{3} (w) - \frac{1}{3} \cdot \log_{3} (y) + 7 \log_{3} (x)$

Step 1

Simplify each term.

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Step 1.1

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

$\log_{3} (w^{3}) - \frac{1}{3} \cdot \log_{3} (y) + 7 \log_{3} (x)$

Step 1.2

Multiply $- \frac{1}{3} \log_{3} (y)$ .

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Step 1.2.1

Reorder $\log_{3} (y)$ and $\frac{1}{3}$ .

$\log_{3} (w^{3}) - (\frac{1}{3} \log_{3} (y)) + 7 \log_{3} (x)$

Step 1.2.2

Simplify $\frac{1}{3} \log_{3} (y)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{3} (w^{3}) - \log_{3} (y^{\frac{1}{3}}) + 7 \log_{3} (x)$

Step 1.3

Simplify $7 \log_{3} (x)$ by moving $7$ inside the logarithm.

$\log_{3} (w^{3}) - \log_{3} (y^{\frac{1}{3}}) + \log_{3} (x^{7})$

Step 2

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

$\log_{3} (\frac{w^{3}}{y^{\frac{1}{3}}}) + \log_{3} (x^{7})$

Step 3

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

$\log_{3} (\frac{w^{3}}{y^{\frac{1}{3}}} x^{7})$

Step 4

Combine $\frac{w^{3}}{y^{\frac{1}{3}}}$ and $x^{7}$ .

$\log_{3} (\frac{w^{3} x^{7}}{y^{\frac{1}{3}}})$