Precalculus Examples

$2 \log (a) - \frac{1}{3} \cdot \log (b) + \log (c)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log (a)$ by moving $2$ inside the logarithm.

$\log (a^{2}) - \frac{1}{3} \cdot \log (b) + \log (c)$

Step 1.2

Multiply $- \frac{1}{3} \log (b)$ .

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Step 1.2.1

Reorder $\log (b)$ and $\frac{1}{3}$ .

$\log (a^{2}) - (\frac{1}{3} \log (b)) + \log (c)$

Step 1.2.2

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

$\log (a^{2}) - \log (b^{\frac{1}{3}}) + \log (c)$

Step 2

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

$\log (\frac{a^{2}}{b^{\frac{1}{3}}}) + \log (c)$

Step 3

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

$\log (\frac{a^{2}}{b^{\frac{1}{3}}} c)$

Step 4

Combine $\frac{a^{2}}{b^{\frac{1}{3}}}$ and $c$ .

$\log (\frac{a^{2} c}{b^{\frac{1}{3}}})$