Precalculus Examples

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

Step 1

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

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Step 1.1

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

$\log_{3} (2 x + y) - (\frac{1}{3} \log_{3} (x - y))$

Step 1.2

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

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

Step 2

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

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