Precalculus Examples

$2 \log_{3} (p) - \frac{1}{2} \cdot \log_{3} (q)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log_{3} (p)$ by moving $2$ inside the logarithm.

$\log_{3} (p^{2}) - \frac{1}{2} \cdot \log_{3} (q)$

Step 1.2

Multiply $- \frac{1}{2} \log_{3} (q)$ .

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Step 1.2.1

Reorder $\log_{3} (q)$ and $\frac{1}{2}$ .

$\log_{3} (p^{2}) - (\frac{1}{2} \log_{3} (q))$

Step 1.2.2

Simplify $\frac{1}{2} \log_{3} (q)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{3} (p^{2}) - \log_{3} (q^{\frac{1}{2}})$

Step 2

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

$\log_{3} (\frac{p^{2}}{q^{\frac{1}{2}}})$