Precalculus Examples

$3 \log_{2} (a) - \frac{1}{4} \log_{2} (b) + \log_{2} (c)$

Step 1

Simplify each term.

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Step 1.1

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

$\log_{2} (a^{3}) - \frac{1}{4} \cdot \log_{2} (b) + \log_{2} (c)$

Step 1.2

Multiply $- \frac{1}{4} \log_{2} (b)$ .

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Step 1.2.1

Reorder $\log_{2} (b)$ and $\frac{1}{4}$ .

$\log_{2} (a^{3}) - (\frac{1}{4} \log_{2} (b)) + \log_{2} (c)$

Step 1.2.2

Simplify $\frac{1}{4} \log_{2} (b)$ by moving $\frac{1}{4}$ inside the logarithm.

$\log_{2} (a^{3}) - \log_{2} (b^{\frac{1}{4}}) + \log_{2} (c)$

Step 2

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

$\log_{2} (\frac{a^{3}}{b^{\frac{1}{4}}}) + \log_{2} (c)$

Step 3

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

$\log_{2} (\frac{a^{3}}{b^{\frac{1}{4}}} c)$

Step 4

Combine $\frac{a^{3}}{b^{\frac{1}{4}}}$ and $c$ .

$\log_{2} (\frac{a^{3} c}{b^{\frac{1}{4}}})$